Radii problems for Ma-Minda Starlikeness

2020/07/15 by Kamaljeet Gangania, Gangania, Kamaljeet, S. Sivaprasad Kumar +1
Mathematics · #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2007.07816

Abstract

For the standard Ma-Minda class S^*(ψ) of univalent starlike functions, we derive S^*(ψ)-radii for some well-known special functions. In addition, we obtain the set of extremal functions for the classical problem max_{f∈ S^*(ψ)}|Φ(log(f(z)/z))| or max_{f∈ S^*(ψ)}\ReΦ(log(f(z)/z)), where Φ is a non-constant entire function. Moreover, we prove certain results on convolution and radius estimates for the case when ψ(\mathbbD) is starlike.

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