Subordination Associated with Laguerre polynomial

TL;DR

This paper investigates the subordination properties of Laguerre polynomials, focusing on their geometric function theory aspects like Janowski starlikeness and convexity, with new results on exponential subordination.

Contribution

It introduces new subordination characteristics of Laguerre polynomials, including exponential subordination and Janowski starlikeness, expanding their geometric function theory understanding.

Findings

Laguerre polynomial satisfies exponential subordination.

Janowski starlikeness and convexity properties are established.

Several examples validate the theoretical results.

Abstract

In this work, we have considered the Laguerre polynomial. This polynomial has been studied in several branches of theoretical physics and applied Mathematics. J. K. Prajapat at.al derived condition so that Laguerre polynomial satisfy convexity, strong starlikeness, close-to-convexity and strongly convexity. In this article, characteristics properties such as exponential subordination have been studied. Moreover Janowski starlikeness and convexity have been investigated for this polynomial. Several examples and corollaries have been mentioned to validates the result.