Meromorphic functions with missing coefficients defined by $q$-derivative

Abstract

By considering a fixed point in the punctured unit disk and using the $q$--derivative, a new subfamily of meromorphic and univalent functions is defined. Also, the first and second order {$q$--derivative} of meromorphic functions are introduced. Coefficient bounds, extreme points, radii of starlikeness and convexity are obtained. Furthermore, the convexity and preserving under convolution with some restrictions on parameters are investigated

Keywords

• meromophic functions
• $q$--derivative
• convex set
• extreme points
• coefficient estimate