Multivalent Functions and Differential Operator Extended by the Quantum Calculus

Abstract

We used the concept of quantum calculus (Jackson’s calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class. The most common inequalities of the proposed functions are geometrically investigated. Our approach was influenced by the theory of differential subordination. As a result, we called attention to a few well-known corollaries of our main conclusions.

Editorial for Special Issue “Recent Advances in Fractional Differential Equations, Delay Differential Equations and Their Applications”

“…This Special Issue contains 17 published papers. In [1], the authors use the concept of quantum calculus (Jackson's calculus) in a recent note to develop an extended class of multivalent functions on the open unit disk. Convexity and star-likeness properties are obtained by establishing conditions for this class.…”