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On the Radius of Univalence and Starlikeness for Certain Analytic Functions


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1 Annamalai University, Annamalainatar, India
     

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Throughout this paper we assume that

(1) f(z) = z+ a2z2 + is analytic for |z| < 1 and

(2) g(z) = z + b2z2 + is analytic and univalent for |z| < 1. Recently T. H. MacGregor [4] determined the radius of univalence of functionsf(z) satisfying |f(z)lg(z) - 1 | < 1, for | z | <1.


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  • On the Radius of Univalence and Starlikeness for Certain Analytic Functions

Abstract Views: 204  |  PDF Views: 0

Authors

K. S. Padmanabhan
Annamalai University, Annamalainatar, India

Abstract


Throughout this paper we assume that

(1) f(z) = z+ a2z2 + is analytic for |z| < 1 and

(2) g(z) = z + b2z2 + is analytic and univalent for |z| < 1. Recently T. H. MacGregor [4] determined the radius of univalence of functionsf(z) satisfying |f(z)lg(z) - 1 | < 1, for | z | <1.