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
Interests: special classes of univalent functions; differential subordinations and superordinations; differential operators; integral operators; differential-integral operators
Special Issues, Collections and Topics in MDPI journals
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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