Sufficient Condition for Geometric properties q-starlikeness and q-convexity of Laguerre Polynomial Function

Document Type : Regular research papers

Authors

1 Department of Mathematics Sangam University, Bhilwara, Rajasthan India

2 Sharad Institute of technology college of Engineering , Yadrav, Maharashtra Sangam University, Bhilwara

10.21608/jfca.2025.290650.1103

Abstract

The geometric properties of q-starlikeness and q-convexity play a pivotal role
in complex analysis, with significant implications in the theory of special functions and
orthogonal polynomials. This paper explores sufficient conditions under which Laguerre
polynomial functions exhibit q-starlikeness and q-convexity. It refers to some coefficient
inequalities, by using this Legurerre polynomial satisfying these geometric properties.
Normalized Legurere Polynomial over the unit disc behaves as a univalent function.
Inequalities applying by Legurerre Polynomial, result in a form of Gauss hypergeometric
function obtained. The geometric properties of q-starlikeness and q-convexity pertain
to the nature of certain functions within the unit disk in the complex plane. For a
function to be q-starlike or q-convex, it needs to satisfy specific conditions related to
its argument and derivatives. The findings contribute to the broader understanding of
geometric properties in special functions, offering a framework for further exploration
and application in various fields of engineering and physics.

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