Revisit Of Meromorphic Convex Functions

TL;DR

This paper investigates sufficient conditions for meromorphically convex functions of order alpha, introduces a new subclass, and analyzes properties related to Schwarzian norms and local univalence.

Contribution

It provides new criteria for meromorphic convexity, introduces a novel subclass, and studies their properties, advancing understanding of meromorphic function behavior.

Findings

Established sufficient conditions for meromorphic convexity

Introduced and characterized a new subclass of meromorphic functions

Analyzed Schwarzian norm properties of locally univalent functions

Abstract

Our primary aim is to explore a sufficient condition for the class of meromorphically convex functions of order $\alpha$, where $0 \leq \alpha < 1$. The investigation will focus on studying a class of continuous functions defined on $[0,1)$, and analyzing the properties of the Schwarzian norm of locally univalent meromorphic functions. Moreover, a new subclass of meromorphic functions is also introduced, and some of its characteristics are examined.