On a Class of Non-Univalent functions Associated with a Parabolic Region

TL;DR

This paper introduces and analyzes a new class of analytic functions linked to a parabolic region in the left-half plane, exploring their geometric properties, radii, majorization, and providing illustrative cases and conditions.

Contribution

It presents a novel class of functions associated with a parabolic region and establishes their geometric properties, radii, majorization results, and sufficient conditions.

Findings

Derived radius and majorization results.

Provided pictorial illustrations of special cases.

Established sufficient conditions for the class.

Abstract

In the present investigation, we introduce and study the geometric properties of a class of analytic functions, associated with a parabolic region majorly lying in the left-half plane. Further we establish radius and majorization results for the class under study with pictorial illustrations of some of its special cases. Also we derive some sufficient conditions for the class under consideration.