NEIGHBOURHOODS OF A SUBCLASS OF UNIFORMLY CONVEX FUNCTIONS

Abstract

In this paper, we investigate the properties of neighbourhoods offunctions for the classes U CV (α) and Sp(α). First we established an inclusion relationship between them and proved a necessary and sufficient conditioninterms of convolutions for a function f to be in Sp(α). Next we show thatthe class Sp(α) is closed under convolution with functions f (z) which are convex univalent. The results obtained in this which generalizes the results ofPadmanabhan [8] and Ronning [9]