Generalizations of Libera integral operator for analytic functions

Abstract

Let 𝒜 p be the class of functions f of the form f(z)=zp+ap+1zp+1+ap+2zp+2+⋯f\left( z \right) = {z^p} + {a_{p + 1}}{z^{p + 1}} + {a_{p + 2}}{z^{p + 2}} + \cdots that are analytic in the open unit disk 𝕌. For f ∈ 𝒜 p, new integral and differential operator nf is considered. The object of the present paper is to discuss some interesting properties of nf and to consider some examples for our results.

Keywords

• libera integral operator
• p-valently starlike function
• p-valently convex function
• convolution
• subordination