The Journal of the Indian Mathematical Society

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On the Radius of Univalence and Starlikeness for Certain Analytic Functions


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1 Department of Mathematics, Andhra University, Waltair, 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)¦g(z) - 1 ] < 1, for ¦ z ¦ < 1.


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

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Authors

K. S. Padmanabhan
Department of Mathematics, Andhra University, Waltair, 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)¦g(z) - 1 ] < 1, for ¦ z ¦ < 1.