On close-to-convex functions of complex orderReport as inadecuate




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International Journal of Mathematics and Mathematical Sciences - Volume 13 1990, Issue 2, Pages 321-330

Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403, OH, USA

Received 15 November 1988

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 Kb of functions close-to-convex of complex order b, b≠0 and its generalization, the classes Knb where n is a nonnegative integer. Here S*b⊂Kb=K0b. Sharp coefficient bounds are determined for Knb as well as several sufficient conditions for functions to belong to Knb. The authors also obtain some distortion and covering theorems for Knb and determine the radius of the largest disk in which every f∈Knb belongs to Kn1. All results are sharp.





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

Source: https://www.hindawi.com/



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