The Journal of the Indian Mathematical Society

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Estimates of Growth for Certain Convex and Close-to-Convex Functions in the Unit DISC


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1 The liamanujan Institute, University of Madras, Madras-5, India
     

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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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  • Estimates of Growth for Certain Convex and Close-to-Convex Functions in the Unit DISC

Abstract Views: 314  |  PDF Views: 0

Authors

K. S. Padmanabhan
The liamanujan Institute, University of Madras, Madras-5, India

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.