Vol. 78, No. 2, 1978

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Radii of convexity for certain classes of univalent analytic functions

O. P. Juneja and M. L. Mogra

Vol. 78 (1978), No. 2, 359–368
Abstract

Let P(α,β) denote the class of functions p(z) = 1 + b1z + which are analytic and satisfy the inequality |(p(z) 1){2β(p(z) α) (p(z) 1)}| < 1 for some α, β (0 α < 1,0 < β 1) and all z E = {z : |z| < 1}. Also, let Pb(α,β) = {p P(α,β) : p(0) = 2(1 α),0 b 1}. In the present paper, we determine sharp estimates for the radii of convexity for functions in the classes Ra(α,β) and Sa(α,β) where Ra(α,β) = {f(z) = z + (1 α)z2 + : f′∈ Pa(α,β),0 a 1}, Sa(α,β) = {g(z) = z + 2(1 α)z2 + : zg∕g Pa(α,β),0 a 1}. The results thus obtained not only sharpen and generalize the various known results but also give rise to several new results.

Mathematical Subject Classification 2000
Primary: 30C45
Milestones
Received: 26 September 1977
Revised: 17 March 1978
Published: 1 October 1978
Authors
O. P. Juneja
M. L. Mogra