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Journal articles on the topic 'Univalent functions'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 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

Silverman, Herb. "Univalent functions having univalent derivatives." Rocky Mountain Journal of Mathematics 16, no. 1 (1986): 55–62. http://dx.doi.org/10.1216/rmj-1986-16-1-55.

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3

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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4

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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5

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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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

Silverman, Herb. "Univalence for convolutions." International Journal of Mathematics and Mathematical Sciences 19, no. 1 (1996): 201–3. http://dx.doi.org/10.1155/s0161171296000294.

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The radius of univalence is found for the convolutionf∗gof functionsf∈S(normalized univalent functions) andg∈C(close-to-convex functions). A lower bound for the radius of univalence is also determined whenfandgrange over all ofS. Finally, a characterization ofCprovides an inclusion relationship.

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8

Ding, Pisheng. "Analytic continuation of generalized trigonometric functions." Proceedings of the American Mathematical Society, Series B 9, no. 5 (2022): 41–49. http://dx.doi.org/10.1090/bproc/119.

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Via a unified geometric approach, certain generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence for the Maclaurin series, commutation with rotation, continuation beyond the domain of univalence, and periodicity.

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9

Amani, Mostafa, Rasoul Aghalary, and Ali Ebadian. "Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications." Journal of Function Spaces 2021 (July 10, 2021): 1–11. http://dx.doi.org/10.1155/2021/4564694.

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In this paper, we study some properties of analytic functions with fixed initial coefficients. The methodology of differential subordination is used for modification and improvements of several well-known results for subclasses of univalent functions by restricting the functions with fixed initial coefficients. Actually, by extending the Nunokawa lemma for fixed initial coefficient functions, we obtain some novel results on subclasses of univalent functions, such as differential inequalities for univalency or starlikeness of analytic functions. Also, we provide some new sufficient conditions f

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10

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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11

Hengartner, W., and G. Schober. "Univalent harmonic functions." Transactions of the American Mathematical Society 299, no. 1 (1987): 1. http://dx.doi.org/10.1090/s0002-9947-1987-0869396-9.

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12

Singh, Gurmeet, Gagandeep Singh, and Gursharn Jit Singh. "A new subclass of univalent functions." Ufimskii Matematicheskii Zhurnal 11, no. 1 (2019): 133–40. http://dx.doi.org/10.13108/2019-11-1-133.

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13

Ahuja, Om P., Sumit Nagpal, and V. Ravichandran. "Radius Constants for Functions with the Prescribed Coefficient Bounds." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/454152.

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For an analytic univalent functionf(z)=z+∑n=2∞anznin the unit disk, it is well-known thatan≤nforn≥2. But the inequalityan≤ndoes not imply the univalence off. This motivated several authors to determine various radii constants associated with the analytic functions having prescribed coefficient bounds. In this paper, a survey of the related work is presented for analytic and harmonic mappings. In addition, we establish a coefficient inequality for sense-preserving harmonic functions to compute the bounds for the radius of univalence, radius of full starlikeness/convexity of orderα (0≤α<1) fo

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14

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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15

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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16

Ahmad El-Faqeer, Ahmad Sulaiman, Zhen Chuan Ng, and Shamani Supramaniam. "On Convolution and Convex Combination of Harmonic Mappings." Journal of Mathematics 2021 (August 10, 2021): 1–12. http://dx.doi.org/10.1155/2021/6553600.

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In this paper, the subclass of harmonic univalent functions by shearing construction is studied and this subclass of harmonic mappings needs a necessary and adequate condition to be convex in the horizontal direction. Furthermore, convolutions of two special subclasses of univalent harmonic mappings are shown to be convex in the horizontal direction. Also, the family of univalent harmonic mappings of the unit disk onto a region convex in the direction of the imaginary axis is introduced. Sufficient conditions for convex combinations of harmonic mappings of this family to be univalently convex

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17

Starkov, V. V. "UNIVALENCE OF HARMONIC FUNCTIONS, PROBLEM OF PONNUSAMY AND SAIRAM, AND CONSTRUCTIONS OF UNIVALENT POLYNOMIALS." Issues of Analysis 21, no. 2 (2014): 59–73. http://dx.doi.org/10.15393/j3.art.2014.2729.

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18

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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19

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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20

Raducanu, Dorina, Horiana Tudor, and Shigeyoshi Owa. "An extension of a basic univalence criterion." Tamkang Journal of Mathematics 44, no. 4 (2013): 417–30. http://dx.doi.org/10.5556/j.tkjm.44.2013.1219.

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Some sufficient conditions for univalence and quasiconformal extension of a class of functions defined by an integral operator are discussed with some examples. This condition involves two arbitrary functions $ g $ and $ h $ analytic in the unit disk. A number of well-known univalent conditions would follow upon specializing the functions and the parameters involved in our main result.

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21

Ruscheweyh, Stephan, and Luis Salinas. "On Convex Univalent Functions with Convex Univalent Derivatives." Rocky Mountain Journal of Mathematics 35, no. 3 (2005): 1017–27. http://dx.doi.org/10.1216/rmjm/1181069719.

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22

Orhan, H., N. Magesh, and V. K. Balaji. "INITIAL COEFFICIENT BOUNDS FOR CERTAIN CLASSES OF MEROMORPHIC BI-UNIVALENT FUNCTIONS." Asian-European Journal of Mathematics 07, no. 01 (2014): 1450005. http://dx.doi.org/10.1142/s1793557114500053.

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In 2010, Srivastava et al. [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett.23(10) (2010) 1188–1192] reviewed the study of coefficient problems for bi-univalent functions. Inspired by the pioneering work of Srivastava et al. [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett.23(10) (2010) 1188–1192], there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions. Motivated largely by Srivastava et al. [Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett.23(

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23

Din, Muhey, Mohsan Raza, and Erhan Deniz. "Univalence criteria for general integral operators involving normalized Dini functions." Filomat 34, no. 7 (2020): 2203–16. http://dx.doi.org/10.2298/fil2007203d.

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In this paper our aim is to deduce some sufficient conditions for integral operators involving normalized Dini functions to be univalent in the open unit disc. The key tools in our proofs are the generalized versions of the well-known Ahlfor?s and Becker?s univalence criteria and some inequalities for the normalized Dini functions.

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24

Aparna, Dr M. "Relation Ship between Classes of Univalent Functions." International journal of Emerging Trends in Science and Technology 03, no. 11 (2016): 4777–83. http://dx.doi.org/10.18535/ijetst/v3i11.09.

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25

Libera, Richard J., and Eligiusz Złotkiewicz. "Bounded Montel univalent functions." Colloquium Mathematicum 56, no. 1 (1988): 169–77. http://dx.doi.org/10.4064/cm-56-1-169-177.

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26

Duren, Peter, and Glenn Schober. "Nonvanishing univalent functions III." Annales Academiae Scientiarum Fennicae. Series A. I. Mathematica 10 (1985): 139–47. http://dx.doi.org/10.5186/aasfm.1985.1016.

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27

Costakis, G., V. Nestoridis, and V. Vlachou. "SMOOTH UNIVALENT UNIVERSAL FUNCTIONS." Mathematical Proceedings of the Royal Irish Academy 107A, no. 1 (2007): 101–14. http://dx.doi.org/10.1353/mpr.2007.0022.

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28

Cruz, Lorena, and Christian Pommerenke. "On concave univalent functions." Complex Variables and Elliptic Equations 52, no. 2-3 (2007): 153–59. http://dx.doi.org/10.1080/17476930601063693.

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29

Jenkins, James A. "On meromorphic univalent functions." Complex Variables, Theory and Application: An International Journal 7, no. 1-3 (1986): 83–87. http://dx.doi.org/10.1080/17476938608814189.

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30

Pommerenke, Ch, and D. Mejìa. "Horocyclically convex univalent functions." Michigan Mathematical Journal 53, no. 3 (2005): 483–96. http://dx.doi.org/10.1307/mmj/1133894160.

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31

Baernstein II, Albert. "Book Review: Univalent functions." Bulletin of the American Mathematical Society 12, no. 1 (1985): 158–66. http://dx.doi.org/10.1090/s0273-0979-1985-15330-3.

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32

Abu-Muhanna, Yusuf, and Glenn Schober. "Nonvanishing meromorphic univalent functions." Proceedings of the American Mathematical Society 104, no. 2 (1988): 487. http://dx.doi.org/10.1090/s0002-9939-1988-0962817-9.

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33

Obradović, Milutin, and Saminathan Ponnusamy. "Product of univalent functions." Mathematical and Computer Modelling 57, no. 3-4 (2013): 793–99. http://dx.doi.org/10.1016/j.mcm.2012.09.004.

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34

Wulan, Hasi. "ON UNIVALENT BLOCH FUNCTIONS." Acta Mathematica Scientia 21, no. 1 (2001): 37–40. http://dx.doi.org/10.1016/s0252-9602(17)30574-x.

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35

Costakis, GG, V. Nestoridis, and V. Vlachou. "Smooth univalent universal functions." Mathematical Proceedings of the Royal Irish Academy 107, no. 1 (2007): 101–14. http://dx.doi.org/10.3318/pria.2007.107.1.101.

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36

Arango, Juan H., Diego Mejía, and Stephan Ruscheweyh. "Exponentially convex univalent functions." Complex Variables, Theory and Application: An International Journal 33, no. 1-4 (1997): 33–50. http://dx.doi.org/10.1080/17476939708815010.

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37

Abu-Muhanna, Yusuf. "On harmonic univalent functions." Complex Variables, Theory and Application: An International Journal 39, no. 4 (1999): 341–48. http://dx.doi.org/10.1080/17476939908815201.

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38

Bhowmik, Bappaditya. "On concave univalent functions." Mathematische Nachrichten 285, no. 5-6 (2011): 606–12. http://dx.doi.org/10.1002/mana.201000063.

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39

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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40

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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41

Frasin, B. A., and M. Darus. "On certain analytic univalent functions." International Journal of Mathematics and Mathematical Sciences 25, no. 5 (2001): 305–10. http://dx.doi.org/10.1155/s0161171201004781.

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We consider the class of analytic functionsB(α)to investigate some properties for this class. The angular estimates of functions in the classB(α)are obtained. Finally, we derive some interesting conditions for the class of strongly starlike and strongly convex of orderαin the open unit disk.

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42

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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43

HERNÁNDEZ, RODRIGO, and MARÍA J. MARTÍN. "Stable geometric properties of analytic and harmonic functions." Mathematical Proceedings of the Cambridge Philosophical Society 155, no. 2 (2013): 343–59. http://dx.doi.org/10.1017/s0305004113000340.

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AbstractGiven any sense preserving harmonic mapping f=h+ḡ in the unit disk, we prove that for all |λ|=1 the functions fλ=h+λḡ are univalent (resp. close-to-convex, starlike, or convex) if and only if the analytic functions Fλ=h+λg are univalent (resp. close-to-convex, starlike, or convex) for all such λ. We also obtain certain necessary geometric conditions on h in order that the functions fλ belong to the families mentioned above. In particular, we see that if fλ are univalent for all λ on the unit circle, then h is univalent.

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44

Lee, See Keong, V. Ravichandran, and Shamani Supramaniam. "Initial Coefficients of Biunivalent Functions." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/640856.

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An analytic functionfdefined on the open unit disk is biunivalent if the functionfand its inversef-1are univalent in𝔻. Estimates for the initial coefficients of biunivalent functionsfare investigated whenfandf-1, respectively, belong to some subclasses of univalent functions. Some earlier results are shown to be special cases of our results.

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45

PESCAR, VIRGIL, and LAURA STANCIU. "Some univalence criteria for a family of integral operators." Creative Mathematics and Informatics 24, no. 2 (2015): 213–19. http://dx.doi.org/10.37193/cmi.2015.02.15.

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The main objective of this paper is to obtain sufficient conditions for a family of integral operators to be univalent in the open unit disk U, using new results on univalence of analytic functions. These integral operators were considered in a recent work, see [Stanciu, L., The univalence conditions of some integral operators, Abstr. Appl. Anal., 2012, Art. ID 924645, 9 pp.].

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46

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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47

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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48

Sokół, Janusz, and Katarzyna Trabka-Wiȩcław. "Radius problems for univalent functions." Journal of Applied Analysis 26, no. 1 (2020): 111–15. http://dx.doi.org/10.1515/jaa-2020-2008.

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AbstractThis paper considers the following problem: for what value r, {r<1} a function that is univalent in the unit disk {|z|<1} and convex in the disk {|z|<r} becomes starlike in {|z|<1}. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

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49

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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50

Gangania, Kamaljeet. "Theory of Certain Non-Univalent Analytic Functions." Mathematica Slovaca 73, no. 5 (2023): 1163–82. http://dx.doi.org/10.1515/ms-2023-0086.

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ABSTRACT We investigate the non-univalent function’s properties reminiscent of the theory of univalent starlike functions. Let the analytic function ψ ( z ) = ∑ i = 1 ∞ A i z i , A 1 ≠ 0 be univalent in the unitdisk. Non-univalent functions may be found in the class ℱ ( ψ ) of analytic functions f of the form f ( z ) = z + ∑ k = 2 ∞ a k z k satisfying (zf′ (z)/f (z) – 1) ≺ ψ(z). Such functions, like the Ma and Minda classes k=2 of starlike functions, also have nice geometric properties. For these functions, growth and distortion theorems have been established. Further, we obtain bounds for som

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