Certain Inclusion Properties for the Class of <i>q</i>-Analogue of Fuzzy <i>α</i>-Convex Functions

Abstract

Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis. We introduce the family of linear q-operators and define various classes associated with these operators. The inclusion results and various integral properties are the main investigations of this article.

Keywords

• analytic functions
• fractional derivative, fuzzy <i>q</i>-starlike functions
• fuzzy <i>q</i>-convex functions
• <i>q</i>-Ruscheweyh derivative operator
• <i>q</i>-Srivastava–Attiya operator