Close-to-convexity and starlikeness of analytic functions

2012/07/27 by Keong, Lee See, V. Ravichandran, Ravichandran, V. +2
Materials Science · Mathematics · #30C45 #30C80 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Polymer Synthesis and Characterization

paper · pdf · doi:10.48550/arxiv.1207.6495

openalex publication_date 2012/07/27 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

For functions f(z)=z^p+a_n+1z^p+1+... defined on the open unit disk, the condition \Re (f'(z)/z^p-1)>0 is sufficient for close-to-convexity of f. By making use of this result, several sufficient conditions for close-to-convexity are investigated and relevant connections with previously known results are indicated.

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