Characterization properties for starlike and convex functions involving a class of fractional integral operators
type: Item
instance of: scholarly article
title: Characterization properties for starlike and convex functions involving a class of fractional integral operators
zbMATH Open document ID: 0907.30015
author: Mamta Bolia
author: Ravinder Krishna Raina
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1999-03-09T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108430
review text: Let \(T_n\) denote the class of functions \(f(z)=z+ \sum^\infty_{k=n+1} a_kz^k\) which are analytic in the unit disc \(U\) and let \(S^*_n\) and \(K_n\) denote the functions \(f\in T_n\) which are, respectively, starlike and convex in \(U\). Using a generalization of the Erdélyi-Kober fractional integral operators in which the \(H\)-function of Fox appears in the kernel, introduced by \textit{V. Kiryakova} [Mat. Vesn. 40, No. 3/4, 259-266 (1988; Zbl 0713.33006)], the authors define a new class of fractional integral operators. In this paper, characterization properties satisfied by this operators of certain analytic functions in \(U\) to be in \(S^*_n\) and \(K_n\) are studied. Characterization theorems associated with the Hadamard product are also proved.
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 33C60
zbMATH DE Number: 1089770
zbMATH Keywords: fractional operator
zbMATH Keywords: starlike function
zbMATH Keywords: convex function
zbMATH Keywords: Hadamard product
reviewed by: O. Fekete
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1089770