Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C4: Complex Analysis".

Deadline for manuscript submissions: 30 November 2026 | Viewed by 533

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 relevant subclasses is an important topic of research in geometric function theory. Since its earliest days, the study of analytic functions has involved the application of numerous operators, among which differential and integral operators are the most remarkable. 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 recent developments by researchers interested in introducing new operators involving complex-valued functions of one or several variables, studying their properties, and applying these newly defined operators in various contexts. Fractional calculus operators have also found significant applications in the theory of analytic functions. Classical definitions of these operators, as well as their generalizations, have led to notable advances in the development and investigation of new function classes exhibiting important geometric properties. In addition to fractional calculus tools and certain hypergeometric functions, elements of quantum calculus have been incorporated into studies of various types of operators. Furthermore, the theories of differential subordination and superordination—together with their more recent extensions, including strong and fuzzy differential subordination and superordination—have continually generated interesting results involving different classes of operators. 

As a follow-up to the previous edition, this Special Issue welcomes academic contributions on the applications of various operators—such as differential, integral, fractional, or quantum calculus operators—for the introductino of new classes of functions; studies employing differential subordination and superordination techniques in all their forms; and related investigations in other areas of complex analysis. It is hoped that the published contributions will inspire further developments in the theory of complex analysis operators, special classes of analytic functions, and other aspects of 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

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Related Special Issue

Published Papers (3 papers)

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Editorial

Jump to: Research

5 pages, 168 KB  
Editorial
Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions
by Gheorghe Oros
Mathematics 2026, 14(8), 1255; https://doi.org/10.3390/math14081255 - 10 Apr 2026
Abstract
The aim of this Special Issue was to attract valuable developments of researchers interested in introducing new operators that involve complex valued functions of one or several variables, studying their properties, and then using the newly defined operators in various ways [...] Full article

Research

Jump to: Editorial

28 pages, 2486 KB  
Article
Sharpness Estimation of Hankel Determinants and Logarithmic Coefficients for a Family of Analytic Functions Related to a Lung-Shaped Domain
by Mohamed A. Mamon, Shams Alyusof, Rabab Alyusof and Alaa H. El-Qadeem
Mathematics 2026, 14(8), 1240; https://doi.org/10.3390/math14081240 - 8 Apr 2026
Abstract
This investigation introduces a novel family of univalent analytic functions subordinate to lung-shaped domains within the open unit disk. Through rigorous application of subordination theory and systematic analysis, we establish coefficient bounds for the initial five coefficients, derive estimates for Hankel determinants of [...] Read more.
This investigation introduces a novel family of univalent analytic functions subordinate to lung-shaped domains within the open unit disk. Through rigorous application of subordination theory and systematic analysis, we establish coefficient bounds for the initial five coefficients, derive estimates for Hankel determinants of orders two and three, determine bounds for the first four logarithmic coefficients, and derive the bounds of some Zalcman functionals. The lung-shaped domain is characterized by the subordination condition involving a secant-based function, which maps the unit disk onto a geometrically distinctive region exhibiting bilateral symmetry. All obtained bounds are demonstrated to be sharp through the construction of specific extreme functions. Full article
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17 pages, 354 KB  
Article
Exploring Bi-Univalent Classes via q-Derivatives and Bivariate Fibonacci Polynomials
by Aruna Mogarala Guruvaya, Basem Aref Frasin, Ibtisam Aldawish and Sondekola Rudra Swamy
Mathematics 2026, 14(4), 718; https://doi.org/10.3390/math14040718 - 19 Feb 2026
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Abstract
The q-calculus framework has emerged as a powerful tool in geometric function theory, enabling refined analysis of analytic and bi-univalent functions. Inspired by the versatility of the q-derivative operator, this paper introduces a new generalized subclass of bi-univalent functions defined via [...] Read more.
The q-calculus framework has emerged as a powerful tool in geometric function theory, enabling refined analysis of analytic and bi-univalent functions. Inspired by the versatility of the q-derivative operator, this paper introduces a new generalized subclass of bi-univalent functions defined via the q-derivative in combination with generalized bivariate Fibonacci polynomials, which have recently gained significant attention in mathematical research. For functions in this class, we establish bounds on the initial coefficients and provide estimates for the corresponding Fekete–Szegö functional. By appropriate specialization of parameters, our results recover several known findings and, importantly, produce bounds for new subclasses of bi-univalent functions not previously studied. This framework unifies earlier developments while extending the theory to novel, analytically meaningful classes. Full article
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