Starlike integral operators

Sanford S. Miller, Petru T. Mocanu and Maxwell O. Reade

Vol. 79 (1978), No. 1, 157–168

DOI: 10.2140/pjm.1978.79.157

Abstract

Let S^∗ denote the set of all functions f(z) = z + ⋯ univalent and starlike in the unit disc U. The authors show that integral operators of the form

with suitable restrictions on the analytic functions Φ(z) and φ(z), for suitable choices of the constants α, β, γ, and δ, transforms S^∗ into S^∗. With other restrictions on the parameters, the authors obtain transformations of the sets K, S^∗×K, K ×K into S^∗. Here K denotes, as usual, the set of all f(z) = z + ⋯ univalent and convex in U.

Mathematical Subject Classification 2000

Primary: 30C45

Milestones

Received: 21 January 1978

Published: 1 November 1978