The Journal of the Indian Mathematical Society

Abstract

Let S denote the class of all univalent analytic functions f defined in the unit disc and normalised by the conditions f(0) = 0,f'(0) = 1. For a fixed α, 0 < α < 1, let C(α) denote the sub-class of S, consisting of all functions f satisfying the differential inequality

Re {z f"/f'}+1>α for |z| <1.

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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.

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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.

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Abstract

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