Bulletin of the Australian Mathematical Society

Table of Contents - 1984 - Volume 29, Issue 01  

Research Article

Analytic mappings with negative coefficients in the unit disc

M.L. Mograa1

a1 School of Mathematical Sciences, University of Khartoum, P0 Box 321, Khartoum, Sudan.

Abstract

Let S0004972700021298_inline1 be analytic in the unit disc U(|z| <1) and let F(z) = (l-λ)f (Z) + λ(f(z)*h(z)) where S0004972700021298_inline2 with cn 's are known and are nonnegative, λ ≥ 0 In the present paper, using convolution methods we investigate the mapping properties of F(z) when f(z) belongs respectively to several subclasses of analytic functions with negative coefficients.

(Received October 10 1983)