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Journal articles on the topic 'FEKETE-SZEGO COEFFICIENT FUNCTIONAL'

Author: Grafiati

Published: 11 September 2023

Last updated: 31 July 2025

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1

R.A Bello. "Coefficient Estimate for a Subclass ofAnalytic Functions Defined by aGeneralizedDifferential Operator." International Journal of Advances in Scientific Research and Engineering 09, no. 07 (2023): 60–70. http://dx.doi.org/10.31695/ijasre.2023.9.7.8.

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The purpose of this paper is to study the coefficient estimates of the class of functions in ()consisting of starlike functions. The sharp upper bounds for the initial coefficients and the Fekete-Szego functional of the functions in the class were established using the Opoola Differential Operator

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2

Chinthamani. S. "Coefficient Estimates for New Subclasses of m – fold Symmetric Functions Associated with Sakaguchi Type Function." Journal of Information Systems Engineering and Management 10, no. 3 (2025): 1094–103. https://doi.org/10.52783/jisem.v10i3.6734.

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This paper presents two new subclasses of the class of m - fold symmetric bi univalent Sakaguchi sort of functions on the open unit disc. For functions in these new subclasses, we derive initial coefficient estimates of the Fekete - Szego and Taylor - Maclaurin functional problems.

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3

Hamzat, Jamiu Olusegun. "Coefficient Bounds for Bazilevic Functions Associated with Modified Sigmoid Function." Asian Research Journal of Mathematics 5, no. 3 (2017): 1–10. https://doi.org/10.9734/ARJOM/2017/33818.

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The focus of the present paper is to obtain the sharp upper bounds of <em>a<sub>2 </sub></em>(α<em>)</em> and <em>a<sub>3 </sub></em>(α<em>)</em> for functions belonging to the Bazilevic class <em>B</em>(<em>α,n,γ,ø</em>) associated with modified sigmoid function. The connection of these bounds to the celebrated Fekete-Szego functional | <em>a<sub>3</sub></em>(α<em>)-</em> <em>µa<sup>2</sup><sub>2</sub></em><sub> </sub>(α<em>)</em>| follows as simple consequence.

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4

SR, Swamy, and Waggas Galib Atshan. "Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials." Gulf Journal of Mathematics 13, no. 2 (2022): 67–77. http://dx.doi.org/10.56947/gjom.v13i2.723.

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Making use of Gegenbauer polynomials, we initiate and explore two sets of normalized regular and bi-univalent (or bi-Schlicht) functions in the unit disc linked with Gegenbauer polynomials. We investigate certain coefficients bounds and the Fekete-Szego functional for functions in these families. We also present few interesting observations and provide relevant connections of the results investigated.

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5

Ahmad, Qazi, Nazar Khan, Mohsan Raza, Muhammad Tahir, and Bilal Khan. "Certain q-difference operators and their applications to the subclass of meromorphic q-starlike functions." Filomat 33, no. 11 (2019): 3385–97. http://dx.doi.org/10.2298/fil1911385a.

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The main aim of this work is to find some coefficient inequalities and sufficient condition for some subclasses of meromorphic starlike functions by using q-difference operator. Here we also define the extended Ruscheweyh differential operator for meromorphic functions by using q-difference operator. Several properties such as coefficient inequalities and Fekete-Szego functional of a family of functions are investigated.

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6

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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7

El-Deeb, Sheza M., and Luminita-Ioana Cotîrlă. "Coefficient Estimates for Quasi-Subordination Classes Connected with the Combination of q-Convolution and Error Function." Mathematics 11, no. 23 (2023): 4834. http://dx.doi.org/10.3390/math11234834.

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We utilize quasi-subordination to analyze and introduce several new classes, and we construct a new operator by combining the error function and q-convolution. Additionally, we obtain estimates for the Fekete Szego functional and the Taylor–Maclaurin coefficients for functions in c2 and c3 new classes. Moreover, we discuss some applications of the operator.

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8

Panigrahi, Trailokya, and Janusz Sokól. "Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli." Boletim da Sociedade Paranaense de Matemática 37, no. 4 (2018): 83–95. http://dx.doi.org/10.5269/bspm.v37i4.32701.

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In this paper, a new subclass of analytic functions ML_{\lambda}^{*} associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}| for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

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9

Srivastava, Hari M., Daniel Breaz, Shahid Khan, and Fairouz Tchier. "Certain New Applications of Symmetric q-Calculus for New Subclasses of Multivalent Functions Associated with the Cardioid Domain." Axioms 13, no. 6 (2024): 366. http://dx.doi.org/10.3390/axioms13060366.

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In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-convex functions. We examine a wide range of interesting properties for functions that can be classified into these newly defined classes, such as estimates for the bounds for the first two coefficients, Fekete–Szego-type functional and coefficient inequalities. All the results found in this research are sharp. A number of well-known corollaries are a

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10

Swarup, Chetan. "Sharp Coefficient Bounds for a New Subclass of q-Starlike Functions Associated with q-Analogue of the Hyperbolic Tangent Function." Symmetry 15, no. 3 (2023): 763. http://dx.doi.org/10.3390/sym15030763.

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In this study, by making the use of q-analogous of the hyperbolic tangent function and a Sălăgean q-differential operator, a new class of q-starlike functions is introduced. The prime contribution of this study covers the derivation of sharp coefficient bounds in open unit disk U, especially the first three coefficient bounds, Fekete–Szego type functional, and upper bounds of second- and third-order Hankel determinant for the functions to this class. We also use Zalcman and generalized Zalcman conjectures to investigate the coefficient bounds of a newly defined class of functions. Furthermore,

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11

Rathi, Sidik, and Shaharuddin Cik Soh. "The Fekete-Szego Theorem for Close-to-convex Functions Associated with The Koebe Type Function." General Mathematics 29, no. 2 (2021): 127–36. http://dx.doi.org/10.2478/gm-2021-0019.

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Abstract This paper deals with the class S containing functions which are analytic and univalent in the open unit disc U = {z ∈ ℂ : |z| < 1}. Functions f in S are normalized by f(0) = 0 and f′(0) = 1 and has the Taylor series expansion of the form f ( z ) = z + ∑ n = 2 ∞ a n z n f\left( z \right) = z + \sum\limits_{n = 2}^\infty {{a_n}{z^n}} . In this paper we investigate on the subclass of S of close-to-convex functions denoted as C gα (λ, δ) where function f ∈ C gα (λ, δ) satisfies Re { e i λ z f ′ ( z ) g α ( z ) } {\mathop{\rm Re}\nolimits} \left\{ {{e^{i\lambda }}{{zf'\left( z \right)}

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12

Al-Ameedee, Sarah A., Mohammed Baqer Hashim Al-Hakeem, and Ali Kadhim Hussein Alghafil. "Fekete-Szego inequalities for higher-order derivatives of multivalent analytic function with application to stealth combat aircraft." Journal of Interdisciplinary Mathematics 27, no. 4 (2024): 721–27. http://dx.doi.org/10.47974/jim-1757.

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In this paper, we find bounds for the Fekete-Szegö coefficient functional for the P-valent Function with Higher Order Derivatives of a new subclass μqp (h) in the open unit disc, U. One of the most crucial strategic requirements for defense and space applications is reducing an object’s visibility to the electromagnetic spectrum used for interrogation. The current method relies on Radar cross-section (RCS) for detection by adopting optimized physical designs that consider reflections and scattering from various edges and corners.

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13

Sivasubramanian, S., and P. Gurusamy. "The Fekete–Szegö coefficient functional problems for q-starlike and q-convex functions related with lemniscate of Bernoulli." Asian-European Journal of Mathematics 12, no. 02 (2019): 1950019. http://dx.doi.org/10.1142/s1793557119500190.

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The area of [Formula: see text]-calculus has attracted the serious attention of researchers. This great interest is due its application in various branches of mathematics and physics. The application of [Formula: see text]-calculus was initiated by Jackson [Jackson, On [Formula: see text]-definite integrals, Quart. J. Pure Appl. Math. 41 (1910) 193–203; On [Formula: see text]-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh 46 (1908) 253–281.], who was the first to develop [Formula: see text]-integral and [Formula: see text]-derivative in a systematic way. In this paper,

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14

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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15

Kowalczyk, Bogumiła, Adam Lecko, and H. M. Srivastava. "A note on the Fekete-Szegö problem for close-to-convex functions with respect to convex functions." Publications de l'Institut Math?matique (Belgrade) 101, no. 115 (2017): 143–49. http://dx.doi.org/10.2298/pim1715143k.

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We discuss the sharpness of the bound of the Fekete-Szego functional for close-to-convex functions with respect to convex functions. We also briefly consider other related developments involving the Fekete-Szego functional |a3 ??a22| (0 ? ? ? 1) as well as the corresponding Hankel determinant for the Taylor-Maclaurin coefficients {an}n?N\{1} of normalized univalent functions in the open unit disk D, N being the set of positive integers.

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16

Ashok Kumar Sahoo, Laxmipriya Parida, and Ashok Kumar Sahoo. "Coefficients Bounds on a Certain Class of Multivalent Analytic Functions." Journal of Mathematics and Computing Science 8, no. 2 (2022): 88–101. https://doi.org/10.24191/jmcs.v8i2.6995.

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In the present work a sub-class is defined by using a linear operator and obtained sufficient condition in terms of the coefficients to be a member of this class. Furthermore, the Fekete-Szego problem is completely solved and foundthat the functional is bounded. Finally, the sharpness of the associated estimatesis also studied.

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17

A., A. Yusuf, and Darus M. "On Q beta-pseudo starlike functions." Asia Mathematika 8, no. 3 (2025): 1–9. https://doi.org/10.5281/zenodo.14775943.

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This study introduced a new concept of a class of  Q beta-pseudo starlike functions with change of notation of the class introduced in [4], using the Quantum approach, involving q-derivative and its integral with investigation of the properties: inclusion, conditions for univalency, coefficient and Fekete-Szego inequalities. Our results are accompanied by their corollaries and implications, which also extend earlier results.

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18

Amourah, Ala, Dunia Jarwan, Jamal Salah, M. J. Mohammed, S. A. Meqdad, and Nidal Anakira. "Euler Polynomials and Bi-univalent Functions." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1948–58. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5314.

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Our research introduces new subclasses of analytical functions that are defined by Euler polynomials. We then proceed to estimate the Fekete-Szego functional problem and the Maclaurin coefficients for this specific subfamily, denoted as |a2| and |a3|. Furthermore, we demonstrate several new results that emerge when we specialize the parameters used in our main findings.

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19

Gul, Ihtesham, Sa’ud Al-Sa’di, Khalida Inayat Noor, and Saqib Hussain. "On a Subfamily of q-Starlike Functions with Respect to m-Symmetric Points Associated with the q-Janowski Function." Symmetry 15, no. 3 (2023): 652. http://dx.doi.org/10.3390/sym15030652.

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The main objective of this paper is to study a new family of analytic functions that are q-starlike with respect to m-symmetrical points and subordinate to the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego functional |a3−μa22| and convolution properties for the functions belonging to this new class. Several consequences of main results are also obtained.

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20

Alnajar, Omar, Omar Khabour, Ala Amourah, and Maslina Darus. "The Relationship of Borel Distribution and Horadam Polynomials Leads to Analytical Bi-Univalent Functions." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5929. https://doi.org/10.29020/nybg.ejpam.v18i2.5929.

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The Borel distribution is a practical and applicable model for a wide range of real-world applications. Using the Borel distribution as a foundation, we create a novel subclass of analytic bi-univalent functions in this study. We employ these functions, which involve the ultraspherical polynomials, to create our new subclass. For functions that fall within the constructed class,we investigate alternative estimations of the Maclaurin coefficients and solve the Fekete-Szego functional problem.

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21

Hamzat, Jamiu Olusegun, and Malik Adekunle Olayiwola. "Initial Coefficients Estimates for Certain Generalized Class of Analytic Functions Involving Sigmoid Function." Asian Research Journal of Mathematics 5, no. 3 (2017): 1–11. https://doi.org/10.9734/ARJOM/2017/33819.

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For function <em>F</em> <sub><em>a</em>,<em>n</em> </sub>(<em>Z</em>)of Bazilevic type, initial coefficients | <em>a<sub> j</sub></em><sub>+1</sub>(α<em>)</em> | , | <em>a<sub> j</sub></em><sub>+2</sub>(α<em>)</em> | and | <em>a<sub> j</sub></em><sub>+3</sub>(α<em>)</em>| for certain generalized class of analytic functions involving logistic sigmoid function are obtained. Further, the Fekete-Szego functional | <em>a<sub> j</sub></em><sub>+2</sub>(α<em>)-</em> <em>µa<sup>2</sup><sub>j</sub></em><sub>+1</sub>(α<em>)</em>| is also considered for functions belonging to the said class of analytic f

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22

Alnajar, Omar, Ala Amourah, Jamal Salah, and Maslina Darus. "Fekete-Szegö Functional Problem for Analytic and Bi-Univalent Functions Subordinate to Gegenbauer Polynomials." Contemporary Mathematics, December 2, 2024, 5731–42. https://doi.org/10.37256/cm.5420245636.

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This article aims to introduce a new qualitative subclass of bi-univalent and analytic functions that are intricately linked to Gegenbauer polynomials. These polynomials, known for their significant role in various areas of mathematics, provide a robust framework for exploring the properties of analytic functions. In our exploration, we will address the Fekete-Szego problem, which is pivotal in the field of complex analysis. By doing so, we will derive the coefficient bounds |h2| and |h3| for functions within this newly defined subclass, thereby enhancing our understanding of their behavior. F

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23

A. M., GBOLAGADE,, ASIRU, T. M., and AWOLERE, I. T. "Coefficient Bounds of Bi-Univalent Function Involving Pseudo-Starlikeness Associatedwith Sigmoid Function Defined by Salagean Operator via Chebyshev Polynomial." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 12, no. 01 (2024). http://dx.doi.org/10.47191/ijmcr/v12i1.05.

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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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