Complex Analysis and Geometric Function Theory, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 8740

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Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Interests: complex analysis; geometric function theory
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Dear Colleagues,

The Special Issue Complex Analysis and Geometric Function Theory endeavors to publish research papers of the highest quality with an appeal for specialists in the field of complex analysis and geometric aspects of complex analysis, and to the broad mathematical community. We hope that the distinctive aspects of the Special Issue will bring the reader closer to the subject of the current research and pave the way for a more direct and less ambivalent approach to the topic.

Our goal is to invite authors to present their original articles, as well as review articles, that will stimulate the continuing efforts in developing new results in these areas of interest. We would hope that this Special Issue will have a great impact on other people in their efforts to broaden their knowledge and investigation and help researchers to summarize the most recent developments and ideas in these fields.

This Special Issue will invite authors to present their original articles that provide not only new results or methods, but also those that may have a great impact on other people in their efforts to broaden their knowledge and investigation. 

Prof. Dr. Teodor Bulboacă
Guest Editor

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Keywords

  • harmonic functions univalent functions meromorphic functions differential subordination and superordination
  • complex polynomials
  • special functions and its applications in geometric function theory
  • quantum calculus and its applications in geometric function theory
  • operators on function spaces
  • Nevanlinna theory
  • quasiconformal maps

Published Papers (11 papers)

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Research

13 pages, 298 KiB  
Article
On the Zeros of the Differential Polynomials φfl(f(k))na
by Jiantang Lu and Junfeng Xu
Mathematics 2024, 12(8), 1196; https://doi.org/10.3390/math12081196 - 16 Apr 2024
Viewed by 149
Abstract
Letting f be a transcendental meromorphic function, we consider the value distribution of the differential polynomials φfl(f(k))na, where φ(0) is a small function of f, [...] Read more.
Letting f be a transcendental meromorphic function, we consider the value distribution of the differential polynomials φfl(f(k))na, where φ(0) is a small function of f, l(2), n(1), k(1) are integers and a is a non-zero constant, and obtain an important inequality concerning the reduced counting function of φfl(f(k))na. Our results improve and generalize the results obtained by Xu and Ye, Karmakar and Sahoo, Chakraborty et.al, and Chen and Huang. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
22 pages, 345 KiB  
Article
On the Study of Starlike Functions Associated with the Generalized Sine Hyperbolic Function
by Baseer Gul, Muhammad Arif, Reem K. Alhefthi, Daniel Breaz, Luminiţa-Ioana Cotîrlă and Eleonora Rapeanu
Mathematics 2023, 11(23), 4848; https://doi.org/10.3390/math11234848 - 01 Dec 2023
Viewed by 698
Abstract
Geometric function theory, a subfield of complex analysis that examines the geometrical characteristics of analytic functions, has seen a sharp increase in research in recent years. In particular, by employing subordination notions, the contributions of different subclasses of analytic functions associated with innovative [...] Read more.
Geometric function theory, a subfield of complex analysis that examines the geometrical characteristics of analytic functions, has seen a sharp increase in research in recent years. In particular, by employing subordination notions, the contributions of different subclasses of analytic functions associated with innovative image domains are of significant interest and are extensively investigated. Since (1+sinh(z))0, it implies that the class Ssinh* introduced in reference third by Kumar et al. is not a subclass of starlike functions. Now, we have introduced a parameter λ with the restriction 0λln(1+2), and by doing that, (1+sinh(λz))>0. The present research intends to provide a novel subclass of starlike functions in the open unit disk U, denoted as Ssinhλ*, and investigate its geometric nature. For this newly defined subclass, we obtain sharp upper bounds of the coefficients an for n=2,3,4,5. Then, we prove a lemma, in which the largest disk contained in the image domain of q0(z)=1+sinh(λz) and the smallest disk containing q0(U) are investigated. This lemma has a central role in proving our radius problems. We discuss radius problems of various known classes, including S*(β) and K(β) of starlike functions of order β and convex functions of order β. Investigating Ssinhλ* radii for several geometrically known classes and some classes of functions defined as ratios of functions are also part of the present research. The methodology used for finding Ssinhλ* radii of different subclasses is the calculation of that value of the radius r<1 for which the image domain of any function belonging to a specified class is contained in the largest disk of this lemma. A new representation of functions in this class, but for a more restricted range of λ, is also obtained. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
27 pages, 361 KiB  
Article
Boundedness and Compactness of Weighted Composition Operators from α-Bloch Spaces to Bers-Type Spaces on Generalized Hua Domains of the First Kind
by Jiaqi Wang and Jianbing Su
Mathematics 2023, 11(20), 4403; https://doi.org/10.3390/math11204403 - 23 Oct 2023
Viewed by 496
Abstract
We address weighted composition operators ψCϕ from α-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and [...] Read more.
We address weighted composition operators ψCϕ from α-Bloch spaces to Bers-type spaces of bounded holomorphic functions on Y, where Y is a generalized Hua domain of the first kind, and obtain some necessary and sufficient conditions for the boundedness and compactness of those operators. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
10 pages, 297 KiB  
Article
Geometric Properties of Certain Classes of Analytic Functions with Respect to (x,y)-Symmetric Points
by Fuad Alsarari, Muhammad Imran Faisal and Alaa Awad Alzulaibani
Mathematics 2023, 11(19), 4180; https://doi.org/10.3390/math11194180 - 06 Oct 2023
Viewed by 556
Abstract
In this article, the present study employs the utilization of the concepts pertaining to (x,y)-symmetrical functions, Janowski type functions, and q-calculus in order to establish a novel subclass within the open unit disk. Specifically, we delve into [...] Read more.
In this article, the present study employs the utilization of the concepts pertaining to (x,y)-symmetrical functions, Janowski type functions, and q-calculus in order to establish a novel subclass within the open unit disk. Specifically, we delve into the examination of convolution properties, which serve as a tool for investigating and inferring adequate and equivalent conditions. Moreover, we also explore specific characteristics of the class S˜qx,y(α,β,λ), thereby further scrutinizing the convolution properties of these newly defined classes. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
14 pages, 446 KiB  
Article
Zeros of Convex Combinations of Elementary Families of Harmonic Functions
by Jennifer Brooks, Megan Dixon, Michael Dorff, Alexander Lee and Rebekah Ottinger
Mathematics 2023, 11(19), 4057; https://doi.org/10.3390/math11194057 - 25 Sep 2023
Viewed by 542
Abstract
Brilleslyper et al. investigated how the number of zeros of a one-parameter family of harmonic trinomials varies with a real parameter. Brooks and Lee obtained a similar theorem for an analogous family of harmonic trinomials with poles. In this paper, we investigate the [...] Read more.
Brilleslyper et al. investigated how the number of zeros of a one-parameter family of harmonic trinomials varies with a real parameter. Brooks and Lee obtained a similar theorem for an analogous family of harmonic trinomials with poles. In this paper, we investigate the number of zeros of convex combinations of members of these families and show that it is possible for a convex combination of two members of a family to have more zeros than either of its constituent parts. Our main tool to prove these results is the harmonic analog of Rouché’s theorem. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
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10 pages, 293 KiB  
Article
On Miller–Ross-Type Poisson Distribution Series
by Basem Aref Frasin and Luminiţa-Ioana Cotîrlă
Mathematics 2023, 11(18), 3989; https://doi.org/10.3390/math11183989 - 20 Sep 2023
Viewed by 653
Abstract
The objective of the current paper is to find the necessary and sufficient conditions for Miller–Ross-type Poisson distribution series to be in the classes ST*(γ,β) and KT(γ,β) of analytic functions [...] Read more.
The objective of the current paper is to find the necessary and sufficient conditions for Miller–Ross-type Poisson distribution series to be in the classes ST*(γ,β) and KT(γ,β) of analytic functions with negative coefficients. Furthermore, we investigate several inclusion properties of the class Yσ(V,W) associated of the operator Iα,cε defined by this distribution. We also take into consideration an integral operator connected to series of Miller–Ross-type Poisson distributions. Special cases of the main results are also considered. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
16 pages, 472 KiB  
Article
Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients
by Gangadharan Murugusundaramoorthy, Kaliappan Vijaya and Teodor Bulboacă
Mathematics 2023, 11(13), 2857; https://doi.org/10.3390/math11132857 - 26 Jun 2023
Cited by 2 | Viewed by 832
Abstract
In this article we introduce three new subclasses of the class of bi-univalent functions Σ, namely HGΣ, GMΣ(μ) and GΣ(λ), by using the subordinations with the functions whose coefficients are Gregory [...] Read more.
In this article we introduce three new subclasses of the class of bi-univalent functions Σ, namely HGΣ, GMΣ(μ) and GΣ(λ), by using the subordinations with the functions whose coefficients are Gregory numbers. First, we evidence that these classes are not empty, i.e., they contain other functions besides the identity one. For functions in each of these three bi-univalent function classes, we investigate the estimates a2 and a3 of the Taylor–Maclaurin coefficients and Fekete–Szegő functional problems. The main results are followed by some particular cases, and the novelty of the characterizations and the proofs may lead to further studies of such types of similarly defined subclasses of analytic bi-univalent functions. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
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15 pages, 316 KiB  
Article
Applications of q-Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses
by Ekram E. Ali, Georgia Irina Oros, Shujaat Ali Shah and Abeer M. Albalahi
Mathematics 2023, 11(12), 2705; https://doi.org/10.3390/math11122705 - 14 Jun 2023
Cited by 3 | Viewed by 964
Abstract
In this article, a new linear extended multiplier operator is defined utilizing the q-Choi–Saigo–Srivastava operator and the q-derivative. Two generalized subclasses of q—uniformly convex and starlike functions of order δ—are defined and studied using this new operator. Necessary conditions [...] Read more.
In this article, a new linear extended multiplier operator is defined utilizing the q-Choi–Saigo–Srivastava operator and the q-derivative. Two generalized subclasses of q—uniformly convex and starlike functions of order δ—are defined and studied using this new operator. Necessary conditions are derived for functions to belong in each of the two subclasses, and subordination theorems involving the Hadamard product of such particular functions are stated and proven. As applications of those findings using specific values for the parameters of the new subclasses, associated corollaries are provided. Additionally, examples are created to demonstrate the conclusions’ applicability in relation to the functions from the newly introduced subclasses. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
14 pages, 310 KiB  
Article
Norm Estimates of the Pre-Schwarzian Derivatives for Functions with Conic-like Domains
by Sidra Zafar, Abbas Kareem Wanas, Mohamed Abdalla and Syed Zakar Hussain Bukhari
Mathematics 2023, 11(11), 2490; https://doi.org/10.3390/math11112490 - 29 May 2023
Viewed by 1313
Abstract
The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U, where U is the open unit disk. The pre-Schwarzian as well as Schwarzian derivatives are popular tools for studying the geometric properties of analytic mappings. These can also be used [...] Read more.
The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U, where U is the open unit disk. The pre-Schwarzian as well as Schwarzian derivatives are popular tools for studying the geometric properties of analytic mappings. These can also be used to obtain either necessary or sufficient conditions for the univalence of a function f. Because of the computational difficulty, the pre-Schwarzian norm has received more attention than the Schwarzian norm. It has applications in the theory of hypergeometric functions, conformal mappings, Teichmüller spaces, and univalent functions. In this paper, we find sharp norm estimates of the pre-Schwarzian derivatives of certain subfamilies of analytic functions involving some conic-like image domains. These results may also be extended to the families of strongly starlike, convex, as well as to functions with symmetric and conjugate symmetric points. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
10 pages, 345 KiB  
Article
Logarithmic Coefficients Inequality for the Family of Functions Convex in One Direction
by Ebrahim Analouei Adegani, Ahmad Motamednezhad, Mostafa Jafari and Teodor Bulboacă
Mathematics 2023, 11(9), 2140; https://doi.org/10.3390/math11092140 - 03 May 2023
Cited by 3 | Viewed by 888
Abstract
The logarithmic coefficients play an important role for different estimates in the theory of univalent functions. Due to the significance of the recent studies about the logarithmic coefficients, the problem of obtaining the sharp bounds for the modulus of these coefficients has received [...] Read more.
The logarithmic coefficients play an important role for different estimates in the theory of univalent functions. Due to the significance of the recent studies about the logarithmic coefficients, the problem of obtaining the sharp bounds for the modulus of these coefficients has received attention. In this research, we obtain sharp bounds of the inequality involving the logarithmic coefficients for the functions of the well-known class G and investigate a majorization problem for the functions belonging to this family. To prove our main results, we use the Briot–Bouquet differential subordination obtained by J.A. Antonino and S.S. Miller and the result of T.J. Suffridge connected to the Alexander integral. Combining these results, we give sharp inequalities for two types of sums involving the modules of the logarithmical coefficients of the functions of the class G indicating also the extremal function. In addition, we prove an inequality for the modulus of the derivative of two majorized functions of the class G, followed by an application. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
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9 pages, 289 KiB  
Article
Estimates for the Coefficients of Subclasses Defined by the Bell Distribution of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials
by Ala Amourah, Omar Alnajar, Maslina Darus, Ala Shdouh and Osama Ogilat
Mathematics 2023, 11(8), 1799; https://doi.org/10.3390/math11081799 - 10 Apr 2023
Cited by 3 | Viewed by 876
Abstract
In the real world there are many applications that find the Bell distribution to be a useful and relevant model. One of these is the normal distribution. In this paper, we develop a new subclass of analytic bi-univalent functions by making use of [...] Read more.
In the real world there are many applications that find the Bell distribution to be a useful and relevant model. One of these is the normal distribution. In this paper, we develop a new subclass of analytic bi-univalent functions by making use of the Bell distribution as a building block. These functions involve the Gegenbauer polynomials, and we use them to establish our new subclass. In this study, we solve the Fekete–Szegö functional problem and analyse various different estimates of the Maclaurin coefficients D2 and D3 for functions that belong to the built class. Full article
(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory, 2nd Edition)
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