Pre-Schwarzian norm estimation for functions in the Ma-Minda-type starlike and convex classes

2025/05/03 by Raju Biswas, Biswas, Raju
Mathematics · #30C45 #30C55 #30C80 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2505.01910

openalex publication_date 2025/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish the sharp estimates of the pre-Schwarzian norm of functions f in the Ma-Minda type starlike and convex classes S^*(φ) and C(φ), respectively, whenever φ(z)=3/(3+(α-3)z-αz²) with -3<α≤ 1, φ(z)=(1+z)(1-s z) with -1/3≤ s≤ 1/3 and φ(z)=1+z/((1-z) (1+αz)) with 0≤ α≤ 1/2.

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