Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions

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

Deadline for manuscript submissions: 31 August 2024 | Viewed by 1104

Special Issue Editor


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Guest Editor
Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania
Interests: special classes of univalent functions; differential subordinations and superordinations; differential operators; integral operators; differential-integral operators
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Special Issue Information

Dear Colleagues,

Finding ways to design various operators that preserve classes of univalent functions and using them to define certain relevant subclasses is an important topic of research in geometric function theory. The study of analytic functions has involved the application of numerous operators since its earliest days. The differential and integral operators are the most remarkable of them. Since the early 1900s, a significant number of mathematicians have focused on operators involving functions of one or several complex variables because they make it simpler to develop new classes of univalent functions.

The aim of the present Special Issue is to attract the most recent developments of the researchers interested in introducing new operators involving complex valued functions of one or several variables, studying their properties, and then using the newly defined operators in various ways. Fractional calculus operators have also developed significant applications in the field of analytic functions theory. The classical definition of these operators and their generalizations have provided notable applications in the development and investigation of new function classes with notable geometric features. In addition to fractional calculus tools and certain hypergeometric functions, components of quantum calculus have also been incorporated in the investigations regarding different types of operators. The theories of differential subordination and superordination, alongside their newer forms of strong and fuzzy differential subordination and superordination, have also constantly generated interesting outcomes involving different types of operators.

Academic contributions will be welcome on applications of various operators, such as differential, integral, fractional, or quantum calculus operators, for introducing new classes of functions, for studies involving all types of differential subordination and superordination techniques or for any other investigations in different areas concerning complex analysis. Hopefully, the published material will inspire new developments regarding complex analysis operators, special classes of analytic functions and any other aspects associated with geometric function theory.

Prof. Dr. Gheorghe Oros
Guest Editor

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Keywords

  • analytic function
  • univalent function
  • differential operator
  • integral operator
  • fractional operator
  • q-operator
  • differential subordination
  • differential superordiantion

Published Papers (2 papers)

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Research

15 pages, 659 KiB  
Article
A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via q̧-Calculus
by Abdullah Alsoboh and Georgia Irina Oros
Mathematics 2024, 12(10), 1594; https://doi.org/10.3390/math12101594 - 20 May 2024
Viewed by 252
Abstract
Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q-calculus. The [...] Read more.
Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with q-calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on |α2| and |α3| coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. Full article
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13 pages, 250 KiB  
Article
Bridging the p-Special Functions between the Generalized Hyperbolic and Trigonometric Families
by Ali Hamzah Alibrahim and Saptarshi Das
Mathematics 2024, 12(8), 1242; https://doi.org/10.3390/math12081242 - 19 Apr 2024
Viewed by 542
Abstract
Here, we study the extension of p-trigonometric functions sinp and cosp family in complex domains and p-hyperbolic functions sinhp and the coshp family in hyperbolic complex domains. These functions satisfy analogous relations as their classical counterparts with some unknown properties. We [...] Read more.
Here, we study the extension of p-trigonometric functions sinp and cosp family in complex domains and p-hyperbolic functions sinhp and the coshp family in hyperbolic complex domains. These functions satisfy analogous relations as their classical counterparts with some unknown properties. We show the relationship of these two classes of special functions viz. p-trigonometric and p-hyperbolic functions with imaginary arguments. We also show many properties and identities related to the analogy between these two groups of functions. Further, we extend the research bridging the concepts of hyperbolic and elliptical complex numbers to show the properties of logarithmic functions with complex arguments. Full article
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