Geometric Properties for Subclasses of Multivalent Analytic Functions Associated with q -Calculus Operator

Ekram E. Ali (), Rabha M. El-Ashwah, Abeer M. Albalahi and Rabab Sidaoui
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Ekram E. Ali: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Rabha M. El-Ashwah: Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
Abeer M. Albalahi: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Rabab Sidaoui: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 81451, Saudi Arabia

Mathematics, 2025, vol. 13, issue 23, 1-12

Abstract: This paper presents new subclasses of multivalent analytic functions defined through the q -derivative operator and examines their inclusion properties. By employing the Jackson q -derivative, we construct generalized operators that encompass numerous previously established operators and provide a framework for defining new classes with distinctive analytic features. Our main results are derived using techniques from differential subordination theory for complex-valued functions of one variable. Some applications of Bernardi operator are discussed.

Keywords: analytic function; Hadamard (convolution) product; ?-analogue multiplier-Ruscheweyh operator; ?-catas operator; ?-Bernardi operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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