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Abstract and Applied Analysis
Volume 2014, Article ID 454152, 12 pages
Research Article

Radius Constants for Functions with the Prescribed Coefficient Bounds

1Department of Mathematics, Kent State University, Burton, OH 44021, USA
2Department of Mathematics, Ramanujan College, University of Delhi, Delhi 110 019, India
3Department of Mathematics, University of Delhi, Delhi 110 007, India

Received 19 June 2014; Accepted 16 August 2014; Published 9 September 2014

Academic Editor: Rosihan M. Ali

Copyright © 2014 Om P. Ahuja et al. 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.


For an analytic univalent function in the unit disk, it is well-known that for . But the inequality does not imply the univalence of . This motivated several authors to determine various radii constants associated with the analytic functions having prescribed coefficient bounds. In this paper, a survey of the related work is presented for analytic and harmonic mappings. In addition, we establish a coefficient inequality for sense-preserving harmonic functions to compute the bounds for the radius of univalence, radius of full starlikeness/convexity of order   () for functions with prescribed coefficient bound on the analytic part.