Applications of the <i>q</i>-Sălăgean Differential Operator Involving Multivalent Functions

Abstract

In this article we explore several applications of q-calculus in geometric function theory. Using the method of differential subordination, we obtain interesting univalence properties for the q-Sălăgean differential operator. Sharp subordination results are obtained by using functions with remarkable geometric properties as subordinating functions and considering the conditions of expressions involving the q-Sălăgean differential operator and a convex combination using it.

Keywords

• analytic functions
• multivalent function
• q-derivative
• q-analogue of the Sălăgean differential operator
• differential subordination
• best dominant