On some univalent integral operators
type: Item
instance of: scholarly article
title: On some univalent integral operators
zbMATH Open document ID: 0629.30013
DOI: 10.1016/0022-247X(87)90208-3
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: A new class \(B_{\alpha}[A,B,C,D]\) for \(\alpha >0\), \(-1\leq B<A\leq 1\), \(- 1\leq D<C\leq 1\) a subclass of the class of Bazilevich functions is defined. Closely following the argument in \textit{R. Parvatham} and \textit{T. N. Shanmugam} [Bull Aust. Math. Soc. 28, 207-215 (1983; Zbl 0515.30008)], few lemmas were established. (In fact they were already proved by T. N. Shanmugam and formed part of his Ph. D. thesis.) Using these lemmas some results were established in this paper, mainly it is proved that this class \(B_{\alpha}[A,B,C,D]\) is closed under the transform by the integral operator \[ \{(m+\alpha)z^{-m}\int^{z}_{0}t^{m- 1}f^{\alpha}(t)dt\}^{1/\alpha}. \] The main result was already established in a much more generalized form for the class \(B(\alpha,h_ 1,h_ 2)\) by \textit{T. N. Shanmugam} in Proc. Indian Acad. Sci., Math. Sci. 95, 121-125 (1986; Zbl 0629.30012).
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 4023638
zbMATH Keywords: Bazilevich functions
author: Khalida Inayat Noor
reviewed by: R. Parvatham
MaRDI profile type: Publication
cites work: Convex and Starlike Univalent Functions
cites work: Some extremal problems for certain families of analytic functions I
cites work: Some Classes of Regular Univalent Functions
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cites work: Subclasses of close-to-convex functions
cites work: On Bazilevic Functions
description: scientific article; zbMATH DE number 4023638