A CLASS OF HARMONIC p𝑝, 𝑞q-STARLIKE FUNCTIONS INVOLVING A GENERALIZED p𝑝, 𝑞q-BERNARDI INTEGRAL OPERATOR

Abstract

With the aid of 𝑞-calculus, this paper introduces a new generalized p𝑝, 𝑞q-Bernardi integral operator ℬ^𝑝 𝑛,𝑞𝑓p𝑧q. Then, we define a new subclass of harmonic p𝑝, 𝑞q-starlike functions of complex order associated with the operator ℬ^𝑝 𝑛,𝑞𝑓p𝑧q. For this new subclass, a necessary and sufficient condition, compact and convex combination theorems, a distortion theorem, and extreme points are investigated. Finally, we discuss the weight mean theorem for functions belonging to this class. This research highlights the significant connections between the results presented in this study and previous works.

Keywords

• harmonic functions
• 𝑞-calculus
• p𝑝
• 𝑞q-bernardi integral operator
• distortion bounds
• extreme points
• convex combination