Hölder Inequalities for a Generalized Subclass of Univalent Functions Involving Borel Distributions

Abstract

In this article, by making use of the Borel distributions series, we introduce a new family of normalized holomorphic functions in the open unit disk and investigate necessary and sufficient conditions for functions f to be in this new class. Furthermore, results on the modified Hadamard product, Hölder inequalities, and closure properties under integral transforms and subordination results are discussed in detail.

Keywords

• univalent
• starlike function
• convex function
• coefficient bounds
• convolution properties
• Borel distribution