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Journal articles on the topic 'Univalent function'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

PASCU, MIHAI N., and NICOLAE R. PASCU. "NEIGHBOURHOODS OF UNIVALENT FUNCTIONS." Bulletin of the Australian Mathematical Society 83, no. 2 (2010): 210–19. http://dx.doi.org/10.1017/s0004972710000468.

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AbstractThe main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–Warschawski–Wolff univalence criterion. We also present an application of the main result in terms of Taylor series, and we show that the hypothesis of our main result is sharp.

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2

Olatunji, Sunday Olufemi, Matthew Olanrewaju Oluwayemi, Saurabh Porwal, and Alina Alb Lupas. "On Quasi-Subordination for Bi-Univalency Involving Generalized Distribution Series." Symmetry 16, no. 6 (2024): 773. http://dx.doi.org/10.3390/sym16060773.

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Various researchers have considered different forms of bi-univalent functions in recent times, and this has continued to gain more attention in Geometric Function Theory (GFT), but not much study has been conducted in the area of application of the certain probability concept in geometric functions. In this manuscript, our motivation is the application of analytic and bi-univalent functions. In particular, the researchers examine bi-univalency of a generalized distribution series related to Bell numbers as a family of Caratheodory functions. Some coefficients of the class of the function are o

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3

Kanwal, Bushra, Khalida Inayat Noor, and Saqib Hussain. "Properties of Certain Classes of Holomorphic Functions Related to Strongly Janowski Type Function." Journal of Mathematics 2021 (November 8, 2021): 1–9. http://dx.doi.org/10.1155/2021/1806174.

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Most subclasses of univalent functions are characterized with functions that map open unit disc ∇ onto the right-half plane. This concept was later modified in the literature with those mappings that conformally map ∇ onto a circular domain. Many researchers were inspired with this modification, and as such, several articles were written in this direction. On this note, we further modify this idea by relating certain subclasses of univalent functions with those that map ∇ onto a sector in the circular domain. As a result, conditions for univalence, radius results, growth rate, and several incl

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4

Pescar, Virgil, and Nicoleta Breaz. "Kudriasov Type Univalence Criteria for Some Integral Operators." Abstract and Applied Analysis 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/721932.

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We consider some integral operators defined by analytic functions in the open unit disk and derive new univalence criteria for these operators, using Kudriasov condition for a function to be univalent.

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5

Obradović, Milutin, and Nikola Tuneski. "Univalency of Certain Transform of Univalent Functions." Proceedings of the Bulgarian Academy of Sciences 76, no. 6 (2023): 821–26. http://dx.doi.org/10.7546/crabs.2023.06.01.

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We consider univalency problem in the unit disc $$\mathbb{D}$$ of the function \[g(z)=\frac{(z/f(z))-1}{-a_{2}}, \] where $$f$$ belongs to some classes of univalent functions in $$\mathbb{D}$$ and $$a_{2}=\frac{f''(0)}{2}\neq 0$$.

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6

SILVERMAN, HERB. "PARTIAL SUMS OF A CLASS OF UNIVALENT FUNCTIONS." Tamkang Journal of Mathematics 29, no. 3 (1998): 171–74. http://dx.doi.org/10.5556/j.tkjm.29.1998.4262.

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7

Zadorozhnaya, Olga V., and Vladimir K. Kochetkov. "Application of the Loewner-Kufarev theory to the construction of a parametric set of univalent functions of a certain form." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 75 (2022): 5–22. http://dx.doi.org/10.17223/19988621/75/1.

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This work relates to the theory of Loewner-Kufarev differential equations, which are a part of the geometric function theory. We apply the well-known second Loewner-Kufarev differential equation to construct a parametric family of univalent functions in the unit disk g(z, t) for each fixed non-negative value of the parameter t generalizing the known parametric families. The article also uses various alternative approaches and provides their comparative analysis. The results of the study can be considered as one sufficient condition for the uniqueness of regular functions in a unit disk. Leadin

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8

Soni, Amit, and Deepak Bansal. "Certain geometric properties of generalized Bessel-Maitland function." Studia Universitatis Babes-Bolyai Matematica 68, no. 4 (2023): 789–98. http://dx.doi.org/10.24193/subbmath.2023.4.08.

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"In the present study, we first introduce Generalized Bessel-Maitland function $\mathbb{J}^{\xi }_{\zeta,a}(z)$ and then derive sufficient conditions under which the Generalized Bessel-Maitland function $\mathbb{J}^{\xi}_{\zeta,a}(z)$ have geometric properties like univalency, starlikeness and convexity in the open unit disk $\mathscr{D}$. Keywords: Univalent, starlike, convex and close-to-convex function, subordination, Bessel functions, Bessel-Maitland functions."

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9

Yamashita, Shinji. "Area and length maxima for univalent functions." Bulletin of the Australian Mathematical Society 41, no. 3 (1990): 435–39. http://dx.doi.org/10.1017/s0004972700018311.

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Let S be the family of functions f(z) = z + a2z2 + … which are analytic and univalent in |z| < 1. We find the valueas a function of r 0 < r < 1. The known lower estimate ofis improved. Relations with the growth theorem are considered and the radius of univalence of f(z)/z is discussed.

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10

Rossdy, Munirah, Rashidah Omar, and Shaharuddin Cik Soh. "Bi-Univalent Function Classes Defined by Using an Einstein Function and a New Generalised Operator." Science and Technology Indonesia 8, no. 2 (2023): 195–204. http://dx.doi.org/10.26554/sti.2023.8.2.195-204.

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Let A be the class of all analytic and univalent functions f (z) = z+Σ∞k=2 akzk in the open unit disc D = {z:|z|<1 }. S then represents the classes of every function in A that is univalent in D. For every f ∈ S, there is an inverse f−1. A function f ∈ A in D is categorised as bi-univalent if f and its inverse g = f−1 are both univalent. Motivated by the generalised operator, subordination principle, and the first Einstein function, we present a new family of bi-univalent analytic functions on the open unit disc of the complex plane. The functions contained in the subclasses are used to acco

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11

Oros, Georgia Irina. "Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities." Symmetry 13, no. 5 (2021): 904. http://dx.doi.org/10.3390/sym13050904.

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In their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using a,b,c∈ℝ, c≠0,−1,−2,…. The study done in this paper extends the results on the univalence of the considered function taking a,b,c∈ℂ, with c≠0,−1,−2,… two criteria being stated in the corollaries of the proved theorems. An interpretation of the univalence results from the sets inclusion view is also given, underlining the geometrical properties of the outc

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12

Hu, Zhenyong, Jinhua Fan, and Xiaoyuan Wang. "Univalence criteria for locally univalent analytic functions." Ukrains’kyi Matematychnyi Zhurnal 75, no. 7 (2023): 987–94. http://dx.doi.org/10.37863/umzh.v75i7.7222.

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UDC 517.5 Suppose that p ( z ) = 1 + z ϕ ' ' ( z ) / ϕ ' ( z ) , where ϕ ( z ) is a locally univalent analytic function in the unit disk D with ϕ ( 0 ) = ϕ ' ( 1 ) - 1 = 0. We establish the lower and upper bounds for the best constants σ 0 and σ 1 such that e - σ 0 / 2 < | p ( z ) | < e σ 0 / 2 and | p ( w ) / p ( z ) | < e σ 1 for z , w ∈ D , respectively, imply the univalence of ϕ ( z ) in D .

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13

Shu Huey, Kiu, Aini Janteng, Jaludin Janteng, and Andy Liew Pik Hern. "Second Hankel Determinant of Bi-univalent Functions." Malaysian Journal of Fundamental and Applied Sciences 19, no. 2 (2023): 269–79. http://dx.doi.org/10.11113/mjfas.v19n2.2807.

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Let be the class of functions which are analytic in the open unit disk and having the form . Denote to be the class for all functions in that are univalent in . Then, let denote the class of bi-univalent functions in . In this paper, we obtain the second Hankel determinant for certain classes of analytic bi-univalent function which are defined by subordinations in the open unit disk . In particular, we determine the initial coefficients and and obtained the upper bound for the functional of functions in the classes of analytic bi-univalent function which are defined by subordinations in .

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14

Hussein, Dhirgam Allawy Hussein, and Sahar Jaafar Mahmood. "Coefficient Estimates for Some Subclasses of m-Fold Symmetric Bi-univalent Functions Defined by Linear Operator." JOURNAL OF ADVANCES IN MATHEMATICS 20 (March 25, 2021): 115–20. http://dx.doi.org/10.24297/jam.v20i.8976.

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The articles introduces and investigates "two new subclasses of the bi-univalent functions ." These are analytical functions related to the m-fold symmetric function and . We calculate the initial coefficients for all the functions that belong to them, as well as the coefficients for the functions that belong to a field where finding these coefficients requires a complicated method. Between the remaining results, the upper bounds for "the initial coefficients "are found in our study as well as several examples. We also provide a general formula for the function and its inverse in the m-field.

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15

Pishkoo, Amir. "On Use of Meijer's G-functions In The Theory of Univalent Functions." JOURNAL OF ADVANCES IN PHYSICS 11, no. 3 (2015): 3162–70. http://dx.doi.org/10.24297/jap.v11i3.413.

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Using some properties of Meijer's G-functions and univalent functions, in this paper some definitions, transformations and theorems in univalent function theory are discussed and then reformulated in the language of Meijer's G-functions. The starting point is to consider the Koebe function as a Meijerâ€™s G-function.

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16

S, Chinthamani, and Lokesh P. "The Extension of Chebyshev Polynomial Bounds Involving Bazilevic Function." Indian Journal of Science and Technology 16, no. 27 (2023): 2040–46. https://doi.org/10.17485/IJST/v16i27.icrms-207.

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Abstract <strong>Objectives:</strong> To propose a new class of bi-univalent function based on Bazilevic Sakaguchi function using the trigonometric polynomials Tn ( q;eiq ) and to find the Taylor – Maclaurin coefficient inequalities and Fekete – Szego inequality for upper bounds. <strong>Methods:</strong> The Chebychev’s polynomial has vast applications in GFT. The powerful tool called convolution (Or Hadamard product), subordination techniques are used in designing the new class. In establishing the core results, derivative tests, triangle inequality and appro

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17

Hamidi, Samaneh G., Suzeini Abd Halim, and Jay M. Jahangiri. "Faber Polynomial Coefficient Estimates for Meromorphic Bi-Starlike Functions." International Journal of Mathematics and Mathematical Sciences 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/498159.

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We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its inverse are starlike univalent.

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18

Priya, Kuppuraj Divya, and K. Thilagavathi. "Geometric Properties of Harmonic Function Affiliated With Fractional Operator." International Journal of Analysis and Applications 22 (August 12, 2024): 133. http://dx.doi.org/10.28924/2291-8639-22-2024-133.

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This paper's goal is to discover new results for the harmonic univalent functions G=υ+η defined in the open unit disc ρ={z: |z|<1}. Examining KS indicates the set of all analytic harmonic functions of form G in the open unit disc ρ. The convolution featuring the Mittag-Leffler function and fractional operator is applied to generate the family of harmonic univalent VKS. Motivated by Kamali [9], we present a novel of kamali class with VKS(δ) brand-new class of harmonic univalent functions Pα,β,zγ,δ,ε,ν inspiring inequality. Analysing Mittag-Leffler function convolution with modified tremblay

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19

Gangadharan, Murugusundaramoorthy, Vijaya Kaliyappan, Hijaz Ahmad, K. H. Mahmoud, and E. M. Khalil. "Mapping properties of Janowski-type harmonic functions involving Mittag-Leffler function." AIMS Mathematics 6, no. 12 (2021): 13235–46. http://dx.doi.org/10.3934/math.2021765.

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<abstract><p>In this paper, we examine a connotation between certain subclasses of harmonic univalent functions by applying certain convolution operator regarding Mittag-Leffler function. To be more precise, we confer such influences with Janowski-type harmonic univalent functions in the open unit disc $ \mathbb{D}. $</p></abstract>

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20

Oluwayemi, Matthew Olanrewaju, Sunday Olufemi Olatunji, and Temitope O. Ogunlade. "On Certain Properties of a Univalent Function Associated with Beta Function." Abstract and Applied Analysis 2022 (July 25, 2022): 1–6. http://dx.doi.org/10.1155/2022/8150057.

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Beta function has some applications in differential equations and other areas of sciences and engineering where certain definite integrals are used. However, its applications to univalent functions have not been explored based on the available literature. In this work, therefore, the authors defined a univalent function associated with the beta function B m , n with m , n > 0 . Some geometric properties of the function are discussed.

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21

Olatunji, S.O. "Sigmoid Function in the Space of Univalent lambda -Pseudo Starlike Function with Sakaguchi Type Functions." Journal of Progressive Research in Mathematics 7, no. 4 (2016): 1164–72. https://doi.org/10.5281/zenodo.3977286.

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In this work, the sigmoid function in the space of univalent lambda - peseudo starlike function with Sakaguchi type functions are investigated. The first few coefficient bounds for the class  (s,t,) / were obtained. Also, the relevant connections to Fekete-Szego theorem for this class were briefly discussed. Our results serves as a new generalization in this direction and it gives birth some existing subclasses of functions.

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22

Srivastava, H. M., Müge Sakar, and Güney Özlem. "Some general coefficient estimates for a new class of analytic and bi-univalent functions defined by a linear combination." Filomat 32, no. 4 (2018): 1313–22. http://dx.doi.org/10.2298/fil1804313s.

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In the present paper, we introduce and investigate a new class of analytic and bi-univalent functions f (z) in the open unit disk U. For this purpose, we make use of a linear combination of the following three functions: f(z)/z, f'(z) and z f''(z) for a function belonging to the normalized univalent function class S. By applying the technique involving the Faber polynomials, we determine estimates for the general Taylor-Maclaurin coefficient of functions belonging to the analytic and bi-univalent function class which we have introduced here. We also demonstrate the not-too-obvious behaviour of

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23

Srivastava, H. M., Sevtap Eker, and Rosihan Alic. "Coefficient bounds for a certain class of analytic and bi-univalent functions." Filomat 29, no. 8 (2015): 1839–45. http://dx.doi.org/10.2298/fil1508839s.

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In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk U. By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.

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24

Delphi, Ali Musaddak. "A New Sandwich Theorem Relating to the Generalized Integral Operator for Univalent Analytic Functions." Indian Journal Of Science And Technology 17, no. 32 (2024): 3344–49. http://dx.doi.org/10.17485/ijst/v17i32.1877.

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Objective: To determine subordination, inclusion, superordination and sandwich theorems for new subclass of analytic univalent functions relating to the generalized integral operator, within a unit disk that is open. Methods: The procedures of the proof these theorems which used to find new results for this subject depend on the Lemma1.2 and Lemma1.3 mentioned inside this paper. Finding: The inclusion theorem for new subclass of univalent analytic function convolution with a generalized integral operator and the sandwich theorem were obtained using new findings for the subordination and supero

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25

Yavuz, Tuǧba. "Coefficient estimates for a new subclass of bi-univalent functions defined by convolution." Creative Mathematics and Informatics 27, no. 1 (2018): 89–94. http://dx.doi.org/10.37193/cmi.2018.01.12.

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In this paper we introduce general subclasses of bi-univalent functions by using convolution. Bounds for the first two coefficients |a2| and |a3| for bi-univalent functions in these classes are obtained. The obtained results generalize the results which are given in [Murugusundaramoorthy, G., Magesh, M., Prameela, V., Coefficient bounds for certain subclasses of bi-univalent function, Abstr. Appl. Anal., (2013), Art. ID 573017, 3 pp.] and [Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions, Studia Univ. Babes¸ Bolyai Math., 31 (1986), No. 2, 70–77].

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26

Srutha Keerthi, B., and M. Revathi. "On Certain New Subclass of Sakaguchi Type Function Related to Sigmoid Functions." International Journal of Engineering & Technology 7, no. 4.36 (2018): 766. http://dx.doi.org/10.14419/ijet.v7i4.36.24238.

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The object of the present paper is to obtain initial coefficients | |,| |,| |, upper bounds of | | and second Hankel determinant associated with a class of analytic univalent function of sakaguchi type function related to sigmoid function in the open unit disc ∆. Various authors as Abiodum, Tinuoye Oladipo, Murugusundaramoorthy et. al., and Olatunji have studied sigmoid function for different classes of analytic and univalent functions. Our results serves as a generalisation in this direction and it gives birth some existing subclasses of functions.

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27

Pishkoo, Amir, and Maslina Darus. "The Yukawa Potential Function and Reciprocal Univalent Function." JOURNAL OF ADVANCES IN PHYSICS 3, no. 2 (2013): 197–202. http://dx.doi.org/10.24297/jap.v3i2.2072.

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This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.

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28

Ali, Musaddak Delphi. "A New Sandwich Theorem Relating to the Generalized Integral Operator for Univalent Analytic Functions." Indian Journal of Science and Technology 17, no. 32 (2024): 3344–49. https://doi.org/10.17485/IJST/v17i32.1877.

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Abstract <strong>Objective:</strong> To determine subordination, inclusion, superordination and sandwich theorems for new subclass of analytic univalent functions relating to the generalized integral operator, within a unit disk that is open. <strong>Methods:</strong> The procedures of the proof these theorems which used to find new results for this subject depend on the Lemma1.2 and Lemma1.3 mentioned inside this paper. <strong>Finding:</strong> The inclusion theorem for new subclass of univalent analytic function convolution with a generalized integral operator and t

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29

Aldawish, Ibtisam, Tariq Al-Hawary, and B. A. Frasin. "Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator." Mathematics 8, no. 5 (2020): 783. http://dx.doi.org/10.3390/math8050783.

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Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and |

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30

GBOLAGADE, A. M., T. M. ASIRU, and I. T. AWOLERE. "COEFFICIENT BOUNDS OF BI-UNIVALENT FUNCTION INVOLVING PSEUDO-STARLIKENESS ASSOCIATED WITH SIGMOID FUNCTION DEFINED BY SALAGEAN OPERATOR VIA CHEBYSHEV POLYNOMIAL." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 12, no. 01 (2024): 3955–65. https://doi.org/10.5281/zenodo.10464245.

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Some special classes of univalent functions play an important role in geometric function theory because of their geometric properties. Many of such classes have been introduced and studied; some became well known, for example, the classes of convex, starlike, close to convex, strongly convex and strongly starlike functions. Previous studies by Awolere and Oladipupo (2018) now served as motivation and background to investigate certain classes of analytic, univalent and bi-univalent functions in terms of their coefficient bounds involving salagean and sigmoid functions via Chebyshev poynomial. T

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31

Kirjackis, J. "On the Existence of Functions being Univalent in Half-plane together with their Derivatives." Nonlinear Analysis: Modelling and Control 6, no. 2 (2001): 43–50. http://dx.doi.org/10.15388/na.2001.6.1.15214.

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In articles [1]-[3] a class of functions being univalent in unit disc with all their derivatives was investigated. It was proved such functions exist and must be the entire functions of exponential type. The example of such a function is an exponential function f(z) = ez. In this work the question on existence of functions, beeing univalent in half-plane with all their derivatives was raised and the negative answer to such question was given.

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32

Alatawi, Abdullah, Maslina Darus, and Badriah Alamri. "Applications of Gegenbauer Polynomials for Subfamilies of Bi-Univalent Functions Involving a Borel Distribution-Type Mittag-Leffler Function." Symmetry 15, no. 4 (2023): 785. http://dx.doi.org/10.3390/sym15040785.

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In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This operator is utilized to develop new subfamilies of bi-univalent functions via the principle of subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on the estimation of the coefficients |aℓ|(ℓ=2,3) and the Fekete–Szegö inequality for functions belonging to these subfamilies of bi-univalent functions. Several corollaries and implications of the findings are discussed. Overall, this study presents a new

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33

Fadipe-Joseph, Olubunmi A., M. O. Oluwayemi, and E. O. Titiloye. "Subclasses of Univalent Functions Involving Modified Sigmoid Function." International Journal of Difference Equations 16, no. 1 (2021): 81. http://dx.doi.org/10.37622/ijde/16.1.2021.81-93.

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34

Nizami, Mustafa, and Turaç Taner. "The Fekete-Szegö Problem for Certain Subclass Bi-univalent Functions of Complex Order." Journal of Scientific and Engineering Research 8, no. 1 (2021): 27–37. https://doi.org/10.5281/zenodo.10551791.

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<strong>Abstract</strong> In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions of complex order on the open unit disk in the complex plane. Here, we solve the Fekete-Szegö problem for this function class.

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35

Shakir, Qasim Ali, and Waggas Galib Atshan. "On Third Hankel Determinant for Certain Subclass of Bi-Univalent Functions." Symmetry 16, no. 2 (2024): 239. http://dx.doi.org/10.3390/sym16020239.

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This study presents a subclass of bi-univalent functions within the open unit disk region . The objective of this class is to determine the bounds of the Hankel determinant of order 3, (). In this study, new constraints for the estimates of the third Hankel determinant for the class are presented, which are of considerable interest in various fields of mathematics, including complex analysis and geometric function theory. Here, we define these bi-univalent functions as and impose constraints on the coefficients . Our investigation provides the upper bounds for the bi-univalent functions in thi

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36

MICHALSKA, MAŁGORZATA, and ANDRZEJ M. MICHALSKI. "A GENERALISATION OF THE CLUNIE–SHEIL-SMALL THEOREM." Bulletin of the Australian Mathematical Society 94, no. 1 (2016): 92–100. http://dx.doi.org/10.1017/s0004972715001586.

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Clunie and Sheil-Small [‘Harmonic univalent functions’, Ann. Acad. Sci. Fenn. Ser. A. I. Math.9 (1984), 3–25] gave a simple and useful univalence criterion for harmonic functions, usually called the shear construction. However, the application of this theorem is limited to planar harmonic mappings that are convex in the horizontal direction. In this paper, a natural generalisation of the shear construction is given. More precisely, our results are obtained under the hypothesis that the image of a harmonic function is a union of two sets that are convex in the horizontal direction.

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37

Srutha Keerthi, B., and Bhuvaneswari Raja. "Coefficient Inequality for Certain New Subclasses of Sakaguchi Type Function Related to Sigmoid Functions." International Journal of Engineering & Technology 7, no. 4.36 (2018): 759. http://dx.doi.org/10.14419/ijet.v7i4.36.24236.

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The question of the present paper is to get starting coefficients| | |,| |,| |, upper limits of | and second Hankel determinant related with a class of systematic univalent capacity of sakaguchi compose work identified with sigmoid capacity in the open unit plate ∆. Different creators as Abiodum, Tinuoye Oladipo, Murugu sundaramoorthy et. al., and Olatunji have contemplated sigmoid capacity for various classes of systematic and univalent capacities. Our outcomes fills in as a speculation toward this path and it conceives an offspring some current subclasses of capacities.

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38

Oluwayemi, M. O., B. O. Moses, and J. O. Hamza. "On a Class of Function of Bounded Turning with Negative Coefficients Associated with a Generalized Multiplier Transformation." WSEAS TRANSACTIONS ON MATHEMATICS 21 (February 25, 2022): 71–76. http://dx.doi.org/10.37394/23206.2022.21.11.

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The study of univalent functions and its applications is an hallmark of geometric function theory. Since univalent functions are analytic and has one-to-one mapping, it has a wide range of applications in the fields of studies where transformations (enlargements and reductions) are done. The functions also have angle and orientation preserving properties among other uses. Many authors have defined and studied various classes of univalent functions using different approaches and tools. In this study however, the authors used a generalized multiplier transformation to define a and investigate a

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39

Altınkaya, Şahsene, Sibel Yalçın, and Serkan Çakmak. "A Subclass of Bi-Univalent Functions Based on the Faber Polynomial Expansions and the Fibonacci Numbers." Mathematics 7, no. 2 (2019): 160. http://dx.doi.org/10.3390/math7020160.

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In this investigation, by using the Komatu integral operator, we introduce the new class of bi-univalent functions based on the rule of subordination. Moreover, we use the Faber polynomial expansions and Fibonacci numbers to derive bounds for the general coefficient of the bi-univalent function class.

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Tra̧bka-Wiȩcław, Katarzyna, Paweł Zaprawa, Magdalena Gregorczyk, and Andrzej Rysak. "On the Fekete–Szegö Type Functionals for Close-to-Convex Functions." Symmetry 11, no. 12 (2019): 1497. http://dx.doi.org/10.3390/sym11121497.

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In this paper, we consider two functionals of the Fekete–Szegö type Θ f ( μ ) = a 4 − μ a 2 a 3 and Φ f ( μ ) = a 2 a 4 − μ a 3 2 for a real number μ and for an analytic function f ( z ) = z + a 2 z 2 + a 3 z 3 + … , | z | < 1 . This type of research was initiated by Hayami and Owa in 2010. They obtained results for functions satisfying one of the conditions Re f ( z ) / z > α or Re f ′ ( z ) > α , α ∈ [ 0 , 1 ) . Similar estimates were also derived for univalent starlike functions and for univalent convex functions. We discuss Θ f ( μ ) and Φ f ( μ ) for close-to-convex functions suc

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Amourah, Ala, Basem Frasin, Jamal Salah, and Feras Yousef. "Subfamilies of Bi-Univalent Functions Associated with the Imaginary Error Function and Subordinate to Jacobi Polynomials." Symmetry 17, no. 2 (2025): 157. https://doi.org/10.3390/sym17020157.

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Numerous researchers have extensively studied various subfamilies of the bi-univalent function family utilizing special functions. In this paper, we introduce and investigate a new subfamily of bi-univalent functions, which is defined on the symmetric domain. This subfamily is connected to the Jacobi polynomial through the imaginary error function. We derive the initial coefficients of the Maclaurin series for functions in this subfamily, and analyze the Fekete–Szegő inequality for these functions. Additionally, by specializing the parameters in our main results, we deduce several new and sign

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Amini, Ebrahim, Shrideh Al-Omari, Kamsing Nonlaopon, and Dumitru Baleanu. "Estimates for Coefficients of Bi-Univalent Functions Associated with a Fractional q-Difference Operator." Symmetry 14, no. 5 (2022): 879. http://dx.doi.org/10.3390/sym14050879.

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In the present paper, we discuss a class of bi-univalent analytic functions by applying a principle of differential subordinations and convolutions. We also formulate a class of bi-univalent functions influenced by a definition of a fractional q-derivative operator in an open symmetric unit disc. Further, we provide an estimate for the function coefficients |a2| and |a3| of the new classes. Over and above, we study an interesting Fekete–Szego inequality for each function in the newly defined classes.

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Amini, Ebrahim, Shrideh Al-Omari, Kamsing Nonlaopon, and Dumitru Baleanu. "Estimates for Coefficients of Bi-Univalent Functions Associated with a Fractional q-Difference Operator." Symmetry 14, no. 5 (2022): 879. http://dx.doi.org/10.3390/sym14050879.

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In the present paper, we discuss a class of bi-univalent analytic functions by applying a principle of differential subordinations and convolutions. We also formulate a class of bi-univalent functions influenced by a definition of a fractional q-derivative operator in an open symmetric unit disc. Further, we provide an estimate for the function coefficients |a2| and |a3| of the new classes. Over and above, we study an interesting Fekete–Szego inequality for each function in the newly defined classes.

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Dziok, Jacek, Ravinder Krishna Raina, and Janusz Sokół. "Applications of differential subordinations for norm estimates of an integral operator." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 2 (2017): 281–91. http://dx.doi.org/10.1017/s0308210517000257.

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By considering the norm of a locally univalent function given bywe obtain such norm estimates for an operator of functions involving a convolution structure of convex univalent functions with a subclass of convex functions (defined by subordination). We also obtain some inequalities concerning this norm for functions under a certain fractional integral operator. Some implications of our results are briefly pointed out in the concluding section.

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Mazin Sh.Mahmoud, Abdul Rahman S.Juma, and Raheam A. Mansor Al-Saphory. "Certain Classes of Univalent Functions With Negative Coefficients Defined By General Linear Operator." Tikrit Journal of Pure Science 24, no. 7 (2019): 129–34. http://dx.doi.org/10.25130/tjps.v24i7.469.

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In this study, a subclass of an univalent function with negative coefficients which is defined by anew general Linear operator have been introduced. The sharp results for coefficients estimators, distortion and closure bounds, Hadamard product, and Neighborhood, and this paper deals with the utilizing of many of the results for classical hypergeometric function, where there can be generalized to m-hypergeometric functions. A subclasses of univalent functions are presented, and it has involving operator which generalizes many well-known. Denote A the class of functions f and we have other

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SAKAR, F. MUGE, and H. OZLEM GUNEY. "Coefficient bounds for M-fold symmetric analytic bi-Bazilevič functions using by Faber polynomial expansion." Creative Mathematics and Informatics 29, no. 1 (2020): 81–89. http://dx.doi.org/10.37193/cmi.2020.01.10.

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A function is said to be bi-univalent in the open unit disc D, if both the function f and its inverse are univalent in the unit disc. Besides, a function is said to be bi-Bazilevic in ˘ D, if both the function f and its inverse are Bazilevic there. The behaviour of these types of functions are unpredictable ˘ and not much is known about their coefficients. In this study, we determined coefficient estimates for the Taylor Maclaurin coefficients of the class on m-fold symmetric bi-Bazilevic functions. We also, use the Faber Polynomial expansions to obtain these coefficient estimates associated w

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Pasunoori, Srinivasulu, and Srinivas V. "On Univalent Functions with Negative Coefficients Defined by Mittag-Leffler Function." Online Mathematics Journal 03, no. 02 (2021): 09–15. https://doi.org/10.5281/zenodo.4743395.

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In this paper, we present and carefully examine a new subclass of analytic functions characterized by a differential operator. Moreover, we derive coefficient estimates, extreme points, starlikeness, and radii of close-to-convexity for the aforementioned class. Furthermore, we investigate the integral means inequalities thereof.

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Aouf, Mohamed K., and Adela O. Mostafa. "Certain inequalities of meromorphic univalent functions associated with the Mittag-Leffler function." Journal of Applied Analysis 25, no. 2 (2019): 173–78. http://dx.doi.org/10.1515/jaa-2019-0018.

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Krushkal, Samuel L. "Proof of the Zalcman conjecture for initial coefficients." gmj 17, no. 4 (2010): 663–81. http://dx.doi.org/10.1515/gmj.2010.043.

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Abstract The well-known Zalcman conjecture, which implies the Bieberbach conjecture, states that the coefficients of univalent functions on the unit disk satisfy the inequality for all n > 2, with the equality only for the Koebe function. This conjecture remained open for n > 3. We provide here the proof of this inequality for n = 4, 5, 6. It relies on the holomorphic homotopy of univalent functions and comparison of generated singular conformal metrics in the disk. The extremality of Koebe's function follows from hyperbolic properties.

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Shaba, Timilehin Gideon, Serkan Araci, Babatunde Olufemi Adebesin, Fairouz Tchier, Saira Zainab, and Bilal Khan. "Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limaçon Domain." Fractal and Fractional 7, no. 7 (2023): 506. http://dx.doi.org/10.3390/fractalfract7070506.

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In this present paper, we define a new operator in conjugation with the basic (or q-) calculus. We then make use of this newly defined operator and define a new class of analytic and bi-univalent functions associated with the q-derivative operator. Furthermore, we find the initial Taylor–Maclaurin coefficients for these newly defined function classes of analytic and bi-univalent functions. We also show that these bounds are sharp. The sharp second Hankel determinant is also given for this newly defined function class.

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