Sufficient Condition for Geometric properties q-starlikeness and q-convexity of Laguerre Polynomial Function | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 16, Issue 2, 2025, Pages 1-7 PDF (189.2 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2025.290650.1103 | ||
| Authors | ||
| Seema Kabra* 1; Deepa Amit Karwa2 | ||
| 1Department of Mathematics Sangam University, Bhilwara, Rajasthan India | ||
| 2Sharad Institute of technology college of Engineering , Yadrav, Maharashtra Sangam University, Bhilwara | ||
| 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. | ||
| Keywords | ||
| Univalent function; q-starlike function; q-convex function; q-derivative operator | ||
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