T. Ram REDDY, P. THIRUPATHIREDDY

8494

NEIGHBOURHOODS OF A SUBCLASS OF UNIFORMLY CONVEX FUNCTIONS

NEIGHBOURHOODS OF A SUBCLASS OF UNIFORMLY CONVEX FUNCTIONS

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]
Keywords:

Neighbourhood Subordination, Hadamard Product,

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Konuralp Journal of Mathematics-Cover
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 2013
  • Yayıncı: Mehmet Zeki SARIKAYA
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