Functions starlike with respect to other points
In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. For p≤β<1, let SS*(β) be the class of normalised analytic functions f defined in the open unit disc D such that Rezf′(z)/(f(z)−f(−z))>β, for some z ϵ D. In this paper, we introdu...
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| Format: | Article |
| Language: | en |
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Hindawi Publishing Corporation
1991
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| Online Access: | http://eprints.um.edu.my/17454/1/AbdulHalimS_%281991%29.pdf http://eprints.um.edu.my/17454/ http://dx.doi.org/10.1155/S0161171291000613 |
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| Summary: | In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. For p≤β<1, let SS*(β) be the class of normalised analytic functions f defined in the open unit disc D such that Rezf′(z)/(f(z)−f(−z))>β, for some z ϵ D. In this paper, we introduce 2 other similar classes SC*(β), SSC*(β) as well as give sharp results for the real part of some function for f ϵ SS*(β), SC*(β) and SSC*(β) The behaviour of certain integral operators are also considered. |
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