Subclasses of meromorphically multivalent functions defined by a differential operator

TL;DR

This paper introduces new subclasses of meromorphically multivalent functions defined via a differential operator, exploring their properties including subordination, coefficient bounds, and neighborhoods, enriching the theory of such functions.

Contribution

The paper defines two novel subclasses of meromorphically multivalent functions using a new differential operator and investigates their fundamental properties.

Findings

Established subordination properties of the subclasses

Derived coefficient estimates and convolution properties

Extended the concept of neighborhoods to these subclasses

Abstract

In this paper we introduce and study two new subclasses \Sigma_{\lambda\mu mp}(\alpha,\beta)$ and $\Sigma^{+}_{\lambda\mu mp}(\alpha,\beta)$ of meromorphically multivalent functions which are defined by means of a new differential operator. Some results connected to subordination properties, coefficient estimates, convolution properties, integral representation, distortion theorems are obtained. We also extend the familiar concept of $% (n,\delta)-$neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions.