On close-to-convex functions of complex order

H. S. Al-Amiri and Thotage S. Fernando

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-10

Abstract:

The class S * ( b ) of starlike functions of complex order b was introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the class K ( b ) of functions close-to-convex of complex order b , b ≠ 0 and its generalization, the classes K n ( b ) where n is a nonnegative integer. Here S * ( b ) ⊂ K ( b ) = K 0 ( b ) . Sharp coefficient bounds are determined for K n ( b ) as well as several sufficient conditions for functions to belong to K n ( b ) . The authors also obtain some distortion and covering theorems for K n ( b ) and determine the radius of the largest disk in which every f ∈ K n ( b ) belongs to K n ( 1 ) . All results are sharp.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:840876

DOI: 10.1155/S0161171290000473

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