A note on successive coefficients of convex functions

2016/04/18 by Ming Li, Toshiyuki Sugawa, Li, Ming +1 · 2 citations
Materials Science · Mathematics · #30C45 (Primary) #30C50 (Secondary) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Polymer Synthesis and Characterization

paper · pdf · doi:10.48550/arxiv.1604.04981

openalex publication_date 2016/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we investigate the supremum and the infimum of the functional |a_n+1|-|a_n| for functions, convex and analytic on the unit disk, of the form f(z)=z+a₂z²+a₃z³+…. We also consider the related problem to maximize the functional |a_n+1-a_n| for convex functions f with f"(0)=p for a prescribed p∈[0,2].

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• Coefficient Problems and Sharp Determinant Estimates for the Class S^*_q1
• Coefficient estimates for the class of q-starlike functions

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