Study of the fuzzy q−spiral-like functions associated with the generalized linear operator

Abstract

Nowadays, the subclasses of analytic functions in terms of fuzzy subsets are studied by various scholars and some of these concepts are extended using the $ q- $theory of functions. In this inspiration, we introduce certain subclasses of analytic function by using the notion of fuzzy subsets along with the idea of $ q- $calculus. We present the $ q- $extensions of the fuzzy spiral-like functions of a complex order. We generalize this class using the $ q- $analogues of the Ruscheweyh derivative and Srivastava-Attiya operators. Various interesting properties are examined for the newly defined subclasses. Also, some previously investigated results are deduced as the corollaries of our major results.

Keywords

• analytic functions
• $ q- $spiral-like
• fuzzy $ q- $starlike functions
• fuzzy $ q- $convex functions
• $ q- $ruscheweyh derivative operator
• $ q- $srivastava-attiya operator