Coefficient estimates for the class of q-starlike functions
Abstract
By employing the -difference operator, various classes of -extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these -extensions with convolution operations. Inspired by prior research, this paper delves into the class of -starlike functions defined via convolution. First, we provide comprehensive analysis of its Taylor coefficients by using the Carath\'eodory-Toeplitz Theorem and its corollaries. Precise upper bounds for the initial few coefficients are obtained for real . Furthermore, we analyze both Hankel and Toeplitz determinants by using the foundational results. Second, we establish the upper bounds of its coefficients with the application of Parseval's theorem for -starlike functions when is a complex number.
Cite
@article{arxiv.2508.03223,
title = {Coefficient estimates for the class of q-starlike functions},
author = {Ming Li and Ao-Li Zhu},
journal= {arXiv preprint arXiv:2508.03223},
year = {2025}
}