First order differential subordination for functions with positive real part

2017/03/10 by Om P. Ahuja, Ahuja, O. P., Sushil Kumar +4
Materials Science · Mathematics · #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Polymer Synthesis and Characterization #math.CV #msc:30C45

paper · pdf · doi:10.48550/arxiv.1703.03590

arxiv created 2017/03/10 · openalex publication_date 2017/03/10 · arxiv updated 2017/03/13 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Sharp estimates on β are determined so that an analytic function p defined on the open unit disk in the complex plane normalized by p(0)=1 is subordinate to some well known starlike functions with positive real part whenever 1+βz p'(z), 1+βz p'(z)/p(z), or 1+βz p'(z)/p²(z) is subordinate to √(1+z). Our results provide sharp version of previously known results.

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