A Class of Janowski-Type (<i>p</i>,<i>q</i>)-Convex Harmonic Functions Involving a Generalized <i>q</i>-Mittag–Leffler Function

Abstract

This research aims to present a linear operator Lp,qρ,σ,μf utilizing the q-Mittag–Leffler function. Then, we introduce the subclass of harmonic (p,q)-convex functions HTp,q(ϑ,W,V) related to the Janowski function. For the harmonic p-valent functions f class, we investigate the harmonic geometric properties, such as coefficient estimates, convex linear combination, extreme points, and Hadamard product. Finally, the closure property is derived using the subclass HTp,q(ϑ,W,V) under the q-Bernardi integral operator.

Keywords

• harmonic <i>p</i>-valent functions
• the <i>q</i>-Mittag–Leffler function
• (<i>p</i>,<i>q</i>)-convex functions
• extreme points
• Hadamard product
• closed convex hulls