Successive coefficients for spirallike and related functions

2019/03/25 by Arora, Vibhuti, Ponnusamy, Saminathan, Sahoo, Swadesh Kumar · 1 citation
#30C45 #30C50 #30C55 #30D30 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.10232

Abstract

We consider the family of all analytic and univalent functions in the unit disk of the form f(z)=z+a₂z²+a₃z³+⋯. Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is | |a_n+1|-|a_n| |, for f belonging to the family of γ-spirallike functions of order α. Our particular results include the case of starlike and convex functions of order α and other related class of functions.

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