Functions starlike with respect to other points

S. Abdul Halim

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-6

Abstract:

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. For p ≤ β < 1 , let S S * ( β ) be the class of normalised analytic functions f defined in the open unit disc D such that Re z f ′ ( z ) / ( f ( z ) − f ( − z ) ) > β , for some z ϵ D . In this paper, we introduce 2 other similar classes S C * ( β ) , S S C * ( β ) as well as give sharp results for the real part of some function for f ϵ S S * ( β ) , S C * ( β ) and S S C * ( β ) The behaviour of certain integral operators are also considered.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:620597

DOI: 10.1155/S0161171291000613

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