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

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