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Functions starlike with respect to other points

DOI: 10.1155/s0161171291000613

Keywords: starlike functions of order β , functions starlike with respect to symmetrical points , close-to-convex , integral operators.

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Abstract:

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. For p ¢ ‰ ¤ 2<1, let SS*( 2) be the class of normalised analytic functions f defined in the open unit disc D such that Rezf ¢ € 2(z)/(f(z) ¢ ’f( ¢ ’z))> 2, for some z ¢ € ‰ μ ¢ € ‰D. In this paper, we introduce 2 other similar classes SC*( 2), SSC*( 2) as well as give sharp results for the real part of some function for f ¢ € ‰ μ ¢ € ‰SS*( 2), SC*( 2) and SSC*( 2) The behaviour of certain integral operators are also considered.

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