English

Coefficient estimates for the class of q-starlike functions

Complex Variables 2025-08-12 v2

Abstract

By employing the qq-difference operator, various classes of qq-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these qq-extensions with convolution operations. Inspired by prior research, this paper delves into the class of qq-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 q(0,1)q\in(0,1). 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 qq-starlike functions when qq is a complex number.

Keywords

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}
}
R2 v1 2026-07-01T04:34:46.598Z