NEIGHBOURHOODS OF A SUBCLASS OF UNIFORMLY CONVEX FUNCTIONS

Authors : T. Ram REDDY, P. THIRUPATHIREDDY

Pages : 102-108

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Publication Date : 2014-12-01

Article Type : Research Paper

Abstract :In this paper, we investigate the properties of neighbourhoods offunctions for the classes U CV insert ignore into journalissuearticles values(α); and Spinsert ignore into journalissuearticles values(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 Spinsert ignore into journalissuearticles values(α);. Next we show thatthe class Spinsert ignore into journalissuearticles values(α); is closed under convolution with functions f insert ignore into journalissuearticles values(z); which are convex univalent. The results obtained in this which generalizes the results ofPadmanabhan [8] and Ronning [9]
Keywords : Neighbourhood, Subordination, Hadamard Product