The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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


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

   Subscribe/Renew Journal


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.


Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 281

PDF Views: 0




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

Abstract Views: 281  |  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.