New Trends in Complex Analysis Researches

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (25 November 2022) | Viewed by 18993

Special Issue Editor

Department of Mathematics and Computer Science, University of Oradea, Oradea 410 087, Romania
Interests: univalent functions; harmonic functions; differential subordination and superordination; geometric theory of analytic and non-analytic functions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The new Special Issue aims to bring the newest results of the study on complex valued functions of one or several complex variables. The topic related to several variables was added as a tribute to the memory of the great researcher, Professor Gabriela Kohr from Babeș-Bolyai University, Cluj-Napoca, Romania. She will be missed, but her brilliant ideas will live on and inspire generations to come.

Contributions of scholars studying different aspects regarding complex valued functions are expected concerning original results on holomorphic functions of both one and several variables. For complex valued functions of one variable, classic differential subordination and superordination theories could be considered, as well as special cases of strong differential subordination and superordination and fuzzy differential subordination and superordination theories. Interesting outcomes are likely to appear regarding the addition of special functions to studies. Quantum calculus, which has been proven to offer tremendous applications in geometric function theory, is also expected to provide lines of research. Classical aspects of the star-likeness and convexity of special classes of analytic functions continue to generate successful studies and they are thus also welcome. Any aspects related to the study on holomorphic functions of several variables are valuable to the success of this Special Issue.

This Special Issue aims to put together research regarding complex valued functions of one and several variables and hence push forward the development of both branches, also inspiring parallels between them. 

Prof. Dr. Georgia Irina Oros
Guest Editor

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Keywords

  • Differential subordination
  • Differential superordination
  • Differential operator
  • Integral operator
  • Carathéodory family
  • Loewner chain
  • Loewner PDE
  • Starlike mapping
  • Convex mapping
  • Herglotz vector field

Published Papers (13 papers)

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Research

8 pages, 255 KiB  
Article
On Coefficient Estimates for a Certain Class of Analytic Functions
by Dorina Răducanu
Mathematics 2023, 11(1), 12; https://0-doi-org.brum.beds.ac.uk/10.3390/math11010012 - 20 Dec 2022
Cited by 1 | Viewed by 856
Abstract
In this paper, we consider a subclass SQ of normalized analytic functions f satisfying f(z)>1/2. For the functions in the class SQ, we determine upper bounds for a number of coefficient estimates, [...] Read more.
In this paper, we consider a subclass SQ of normalized analytic functions f satisfying f(z)>1/2. For the functions in the class SQ, we determine upper bounds for a number of coefficient estimates, among which are initial coefficients, the second Hankel determinant, and the Zalcman functional. Upper estimates for higher-order Schwarzian derivatives are also obtained. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
15 pages, 309 KiB  
Article
Coefficient Inequalities for Biholomorphic Mappings on the Unit Ball of a Complex Banach Space
by Hidetaka Hamada, Gabriela Kohr and Mirela Kohr
Mathematics 2022, 10(24), 4832; https://0-doi-org.brum.beds.ac.uk/10.3390/math10244832 - 19 Dec 2022
Viewed by 951
Abstract
In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H. [...] Read more.
In the first part of this paper, we give generalizations of the Fekete–Szegö inequalities for quasiconvex mappings F of type B and the first elements F of g-Loewner chains on the unit ball of a complex Banach space, recently obtained by H. Hamada, G. Kohr and M. Kohr. We obtain the Fekete–Szegö inequalities using the norm under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F. In the second part of this paper, we give the estimation of the difference of the moduli of successive coefficients for the first elements of g-Loewner chains on the unit disc. We also give the estimation of the difference of the moduli of successive coefficients for the first elements F of g-Loewner chains on the unit ball of a complex Banach space under the restrictions on the second and third order terms of the homogeneous polynomial expansions of the mappings F. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
24 pages, 359 KiB  
Article
Sharp Coefficient Problems of Functions with Bounded Turnings Subordinated by Sigmoid Function
by Muhammad Arif, Safa Marwa, Qin Xin, Fairouz Tchier, Muhammad Ayaz and Sarfraz Nawaz Malik
Mathematics 2022, 10(20), 3862; https://0-doi-org.brum.beds.ac.uk/10.3390/math10203862 - 18 Oct 2022
Cited by 3 | Viewed by 879
Abstract
This study deals with analytic functions with bounded turnings, defined in the disk Od=z:z<1. These functions are subordinated by sigmoid function 21+ez and their class is denoted by BTSg [...] Read more.
This study deals with analytic functions with bounded turnings, defined in the disk Od=z:z<1. These functions are subordinated by sigmoid function 21+ez and their class is denoted by BTSg. Sharp coefficient inequalities, including the third Hankel determinant for class BTSg, were investigated here. The same was also included for the logarithmic coefficients related to functions of the class BTSg. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
15 pages, 312 KiB  
Article
Results on Hankel Determinants for the Inverse of Certain Analytic Functions Subordinated to the Exponential Function
by Lei Shi, Hari M. Srivastava, Ayesha Rafiq, Muhammad Arif and Muhammad Ihsan
Mathematics 2022, 10(19), 3429; https://0-doi-org.brum.beds.ac.uk/10.3390/math10193429 - 21 Sep 2022
Cited by 18 | Viewed by 1069
Abstract
In the present paper, we aimed to discuss certain coefficient-related problems for the inverse functions associated with a bounded turning functions class subordinated with the exponential function. We calculated the bounds of some initial coefficients, the Fekete–Szegö-type inequality, and the estimation of Hankel [...] Read more.
In the present paper, we aimed to discuss certain coefficient-related problems for the inverse functions associated with a bounded turning functions class subordinated with the exponential function. We calculated the bounds of some initial coefficients, the Fekete–Szegö-type inequality, and the estimation of Hankel determinants of second and third order. All of these bounds were proven to be sharp. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
15 pages, 331 KiB  
Article
On Geometric Properties of Bessel–Struve Kernel Functions in Unit Disc
by Najla M. Alarifi and Saiful R. Mondal
Mathematics 2022, 10(14), 2516; https://0-doi-org.brum.beds.ac.uk/10.3390/math10142516 - 19 Jul 2022
Cited by 2 | Viewed by 1321
Abstract
The Bessel–Struve kernel function defined in the unit disc is used in this study. The Bessel–Struve kernel functions are generalized in this article, and differential equations are derived. We found conditions under which the generalized Bessel–Struve function is Lemniscate convex by using a [...] Read more.
The Bessel–Struve kernel function defined in the unit disc is used in this study. The Bessel–Struve kernel functions are generalized in this article, and differential equations are derived. We found conditions under which the generalized Bessel–Struve function is Lemniscate convex by using a subordination technique. The relation between the Janowski class and exponential class is also derived. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
18 pages, 343 KiB  
Article
Applications of Subordination Chains and Fractional Integral in Fuzzy Differential Subordinations
by Georgia Irina Oros and Simona Dzitac
Mathematics 2022, 10(10), 1690; https://0-doi-org.brum.beds.ac.uk/10.3390/math10101690 - 15 May 2022
Cited by 17 | Viewed by 1464
Abstract
Fuzzy differential subordination theory represents a generalization of the classical concept of differential subordination which emerged in the recent years as a result of embedding the concept of fuzzy set into geometric function theory. The fractional integral of Gaussian hypergeometric function is defined [...] Read more.
Fuzzy differential subordination theory represents a generalization of the classical concept of differential subordination which emerged in the recent years as a result of embedding the concept of fuzzy set into geometric function theory. The fractional integral of Gaussian hypergeometric function is defined in this paper and using properties of the subordination chains, new fuzzy differential subordinations are obtained. Dominants of the fuzzy differential subordinations are given and using particular functions as such dominants, interesting geometric properties interpreted as inclusion relations of certain subsets of the complex plane are presented in the corollaries of the original theorems stated. An example is constructed as an application of the newly proved results. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
18 pages, 326 KiB  
Article
On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions
by Mohsan Raza, Sarfraz Nawaz Malik, Qin Xin, Muhey U. Din and Luminiţa-Ioana Cotîrlă
Mathematics 2022, 10(9), 1361; https://0-doi-org.brum.beds.ac.uk/10.3390/math10091361 - 19 Apr 2022
Cited by 1 | Viewed by 1127
Abstract
In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk. The main tools for our [...] Read more.
In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk. The main tools for our discussions were the Kudriasov conditions for the univalency of functions, as well as functional inequalities for the generalized Bessel functions. We included the conditions for the univalency of integral operators that involve Bessel, modified Bessel and spherical Bessel functions as special cases. Furthermore, we provided sufficient conditions for the integral operators that involve trigonometric, as well as hyperbolic, functions as an application of our results. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
9 pages, 287 KiB  
Article
New Applications of Gegenbauer Polynomials on a New Family of Bi-Bazilevič Functions Governed by the q-Srivastava-Attiya Operator
by Abbas Kareem Wanas and Luminiţa-Ioana Cotîrlǎ
Mathematics 2022, 10(8), 1309; https://0-doi-org.brum.beds.ac.uk/10.3390/math10081309 - 14 Apr 2022
Cited by 8 | Viewed by 1342
Abstract
In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family JΣ(λ,γ,s,t,q;h) of holomorphic and bi-univalent functions which were defined in the unit disk [...] Read more.
In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family JΣ(λ,γ,s,t,q;h) of holomorphic and bi-univalent functions which were defined in the unit disk D associated with the q-Srivastava–Attiya operator. We establish the bounds for |a2| and |a3|, where a2, a3 are the initial Taylor–Maclaurin coefficients. For the new family of functions JΣ(λ,γ,s,t,q;h) we investigate the Fekete-Szegö inequality, special cases and consequences. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
9 pages, 254 KiB  
Article
Fractional Calculus and Confluent Hypergeometric Function Applied in the Study of Subclasses of Analytic Functions
by Alina Alb Lupaş and Georgia Irina Oros
Mathematics 2022, 10(5), 705; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050705 - 23 Feb 2022
Cited by 2 | Viewed by 997
Abstract
The study done for obtaining the original results of this paper involves the fractional integral of the confluent hypergeometric function and presents its new applications for introducing a certain subclass of analytic functions. Conditions for functions to belong to this class are determined [...] Read more.
The study done for obtaining the original results of this paper involves the fractional integral of the confluent hypergeometric function and presents its new applications for introducing a certain subclass of analytic functions. Conditions for functions to belong to this class are determined and the class is investigated considering aspects regarding coefficient bounds as well as partial sums of these functions. Distortion properties of the functions belonging to the class are proved and radii estimates are established for starlikeness and convexity properties of the class. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
15 pages, 622 KiB  
Article
Subclasses of Multivalent Meromorphic Functions with a Pole of Order p at the Origin
by Daniel Breaz, Kadhavoor R. Karthikeyan and Elangho Umadevi
Mathematics 2022, 10(4), 600; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040600 - 16 Feb 2022
Cited by 4 | Viewed by 1650
Abstract
In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of [...] Read more.
In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. We provide the conditions to obtain sufficient conditions for meromorphic starlikeness involving quasi-subordination. Our other main results include the solution to the Fekete–Szegő problem and inclusion relationships for functions belonging to the defined function classes. Several consequences of our main results are pointed out. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
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11 pages, 297 KiB  
Article
Applications of (M,N)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions
by Abbas Kareem Wanas and Luminiţa-Ioana Cotîrlă
Mathematics 2022, 10(4), 595; https://0-doi-org.brum.beds.ac.uk/10.3390/math10040595 - 14 Feb 2022
Cited by 13 | Viewed by 1873
Abstract
In the current article, making use of certain operator, we initiate and explore a certain family WΣ(λ,γ,σ,δ,α,β,p,q;h) of holomorphic and bi-univalent functions in [...] Read more.
In the current article, making use of certain operator, we initiate and explore a certain family WΣ(λ,γ,σ,δ,α,β,p,q;h) of holomorphic and bi-univalent functions in the open unit disk D. We establish upper bounds for the initial Taylor–Maclaurin coefficients and the Fekete–Szegö type inequality for functions in this family. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
10 pages, 250 KiB  
Article
Certain Properties of a Class of Functions Defined by Means of a Generalized Differential Operator
by Matthew Olanrewaju Oluwayemi, Kaliappan Vijaya and Adriana Cătaş
Mathematics 2022, 10(2), 174; https://0-doi-org.brum.beds.ac.uk/10.3390/math10020174 - 06 Jan 2022
Cited by 5 | Viewed by 1245
Abstract
In this article, we construct a new subclass of analytic functions involving a generalized differential operator and investigate certain properties including the radius of starlikeness, closure properties and integral means result for the class of analytic functions with negative coefficients. Further, the relationship [...] Read more.
In this article, we construct a new subclass of analytic functions involving a generalized differential operator and investigate certain properties including the radius of starlikeness, closure properties and integral means result for the class of analytic functions with negative coefficients. Further, the relationship between the results and some known results in literature are also established. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
12 pages, 284 KiB  
Article
Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions
by Georgia Irina Oros and Luminiţa-Ioana Cotîrlă
Mathematics 2022, 10(1), 129; https://0-doi-org.brum.beds.ac.uk/10.3390/math10010129 - 02 Jan 2022
Cited by 33 | Viewed by 1725
Abstract
The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance [...] Read more.
The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin coefficients |am+1| and |a2m+1| are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes. Full article
(This article belongs to the Special Issue New Trends in Complex Analysis Researches)
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