Functional inequalities for starlike and convex functions associated with $g$-derivative operator

An Huang; Pinhong Long; Halit Orhan; Huo Tang

Functional inequalities for starlike and convex functions associated with $g$-derivative operator

Complex Variables 2026-07-21 v1

Authors: An Huang , Pinhong Long , Halit Orhan , Huo Tang

Abstract

In this paper we first introduce a new class of derivative operators, termed $g$ -derivative operators, which unifies the $q$ -derivative, $(p,q)$ -derivative and $(\alpha,\beta,\gamma)$ -derivative operators, even classical derivative in the literature. Based on this generalized framework, we define two novel function classes, specifically $g$ -starlike functions and $g$ -convex functions. Further, we employ the subordination principle of analytic functions to conduct the coefficient estimations for such function classes, and subsequently derive the bounds for the corresponding Fekete-Szeg\"{o} inequality, Toeplitz determinants and Hankel determinants.

Keywords

g-derivative operator starlike functions convex functions Fekete-Szegő inequality Toeplitz determinants Hankel determinants

Cite

@article{arxiv.2607.18976,
  title  = {Functional inequalities for starlike and convex functions associated with $g$-derivative operator},
  author = {An Huang and Pinhong Long and Halit Orhan and Huo Tang},
  journal= {arXiv preprint arXiv:2607.18976},
  year   = {2026}
}