Radius of starlikeness of p-valent λ-fractional operator

S.M. Aydoğan and F.M. Sakar

Applied Mathematics and Computation, 2019, vol. 357, issue C, 374-378

Abstract: Let consider Ap denoting a class of analytical functions defined as f(z)=zp+ap+1zp+1+⋯+ap+nzp+n+⋯ and p-valent in unit disc U={z||z|<1}. f(z) ∈ Ap is expressed to be p-valently starlike in U if there is a positive figure ρ fulfilling ρ < |z| < 1, Re(zf′(z)f(z))>0, and ∫02πRe(zf′(z)f(z))dθ=2pπ,z=reiθ,ρ < r < 1. Let us consider S*(p) denoting the family of f(z) in Ap, being regular and p-valently starlike in U. It was proved by Goodman [3] that f(z) ∈ S*(p) is at most p-valent in U.

Keywords: Radius of starlikeness; Fractional operator; Convolution (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:357:y:2019:i:c:p:374-378

DOI: 10.1016/j.amc.2018.11.067

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