On a generalization of starlike functions

TL;DR

This paper investigates the properties of a generalized class of starlike functions, focusing on their q-starlikeness, and addresses classical problems like Bieberbach, Fekete-Szeg"o, and Hankel determinants within this context.

Contribution

It introduces a generalized class of starlike functions and explores their q-starlikeness, extending classical geometric function theory results.

Findings

Determined the order of q-starlikeness for basic hypergeometric functions.

Solved the Bieberbach-type problem for the generalized starlike class.

Analyzed Fekete-Szeg"o and Hankel determinant problems for these functions.

Abstract

In this paper, we mainly study the order of $q$-starlikeness of the well-known basic hypergeometric function. In addition, we obtain the Bieberbach-type problem for a generalized class of starlike functions. We also discuss the Fekete-szeg\"o and the Hankel determinant problems for the same class of functions.