Integral Operator of Analytic Functions with Positive Real Part

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 1,  2011, pp.77-85
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.1.077
Title & Authors
Integral Operator of Analytic Functions with Positive Real Part
Frasin, Basem Aref;

Abstract
In this paper, we introduce the integral operator $\small{I_{\beta}}$($\small{p_1}$, $\small{{\ldots}}$, $\small{p_n}$; $\small{{\alpha}_1}$, $\small{{\ldots}}$, $\small{{\alpha}_n}$)(z) analytic functions with positive real part. The radius of convexity of this integral operator when $\small{{\beta}}$ = 1 is determined. In particular, we get the radius of starlikeness and convexity of the analytic functions with Re {f(z)/z} > 0 and Re {f'(z)} > 0. Furthermore, we derive sufficient condition for the integral operator $\small{I_{\beta}}$($\small{p_1}$, $\small{{\ldots}}$, $\small{p_n}$; $\small{{\alpha}_1}$, $\small{{\ldots}}$, $\small{{\alpha}_n}$)(z) to be analytic and univalent in the open unit disc, which leads to univalency of the operators $\small{\int\limits_0^z(f(t)/t)^{\alpha}}$dt and $\small{\int\limits_0^z(f$.
Keywords
Analytic and univalent functions;Starlike and convex functions;Functions of positive real part;Integral operator;
Language
English
Cited by
1.
General Integral Operator of Analytic Functions Involving Functions with Positive Real Part, Journal of Mathematics, 2013, 2013, 1
2.
On General Integral Operator of Analytic Functions, Abstract and Applied Analysis, 2013, 2013, 1
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