Uniformly convex spiral functions and uniformly spirallike functions associated with Pascal distribution series

Abstract

The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes $\mathcal{SP}_p(\alpha,\beta)$ and $\mathcal{UCV}_p(\alpha,\beta)$ of uniformly spirallike functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

Keywords

• analytic function
• hadamard product
• uniformly spirallike function
• pascal distribution series