2025/08/05 by Ming Li, Li, Ming, Zhu, Ao-Li
Mathematics · #30C45 #30C50 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2508.03223
openalex publication_date 2025/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By employing the q-difference operator, various classes of q-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these q-extensions with convolution operations. Inspired by prior research, this paper delves into the class of q-starlike functions defined via convolution. First, we provide comprehensive analysis of its Taylor coefficients by using the Carathéodory-Toeplitz Theorem and its corollaries. Precise upper bounds for the initial few coefficients are obtained for real q∈(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 q-starlike functions when q is a complex number.