Certain subclasses of Spirallike univalent functions related with Pascal distribution series

TL;DR

This paper investigates subclasses of spiral-like univalent functions linked with Pascal distribution series, establishing conditions for their inclusion and exploring related integral operators.

Contribution

It provides necessary and sufficient conditions for Pascal distribution-based subclasses to be spiral-like and examines their properties and inclusion relations.

Findings

Derived conditions for subclasses to be spiral-like

Analyzed inclusion relations within the open unit disk

Studied properties of related integral operators

Abstract

The purpose of the present paper is to find the necessary and sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations for such subclasses in the open unit disk $\mathbb{D}.$ Further, we consider the properties of integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.