Uniformly starlike functions and uniformly convex functions related to the Pascal distribution

Abstract

In this article, we aim to find sufficient conditions for a convolution of analytic univalent functions and the Pascal distribution series to belong to the families of uniformly starlike functions and uniformly convex functions in the open unit disk $\mathbb{U}$. We also state corollaries of our main results.

Keywords

• uniformly starlike function
• uniformly convex function
• starlike function
• convex function
• pascal distribution
• convolution