AI 中文总结
研究与g-导数算子相关的星形和凸函数，通过引入新算子定义新函数类，并利用解析函数从属原理进行系数估计，得出Fekete-Szegö不等式、Toeplitz行列式和Hankel行列式的界。
AI 中文摘要
本文首先引入了一类新的导数算子，称为g-导数算子，它统一了q-导数、(p,q)-导数和(α,β,γ)-导数算子，甚至文献中的经典导数。基于这个广义框架，定义了两个新的函数类，即g-星形函数和g-凸函数。进一步利用解析函数的从属原理对这些函数类进行系数估计，进而得到相应的Fekete-Szegö不等式、Toeplitz行列式和Hankel行列式的界。
英文摘要
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 $(α,β,γ)$-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-Szegö inequality, Toeplitz determinants and Hankel determinants.
