Functions starlike with respect to other points

Functions starlike with respect to other points

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. For p≤β<1, let SS*(β) be the class of normalised analytic functions f defined in the open unit disc D such that Rezf′(z)/(f(z)−f(−z))>β, for some z ϵ D. In this paper, we introdu...

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Bibliographic Details
Main Author: S. Abdul Halim
Format: Article
Language:English
Published: Hindawi Limited 1991-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
starlike functions of order &#946;
functions starlike with respect to symmetrical points
close-to-convex
integral operators.
Online Access:http://dx.doi.org/10.1155/S0161171291000613
Description
Summary:In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. For p≤β<1, let SS*(β) be the class of normalised analytic functions f defined in the open unit disc D such that Rezf′(z)/(f(z)−f(−z))>β, for some z ϵ D. In this paper, we introduce 2 other similar classes SC*(β), SSC*(β) as well as give sharp results for the real part of some function for f ϵ SS*(β), SC*(β) and SSC*(β) The behaviour of certain integral operators are also considered.
ISSN:0161-1712
1687-0425

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