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2014 Radius Constants for Functions with the Prescribed Coefficient Bounds
Om P. Ahuja, Sumit Nagpal, V. Ravichandran
Abstr. Appl. Anal. 2014(SI07): 1-12 (2014). DOI: 10.1155/2014/454152


For an analytic univalent function f ( z ) = z + n = 2 a n z n in the unit disk, it is well-known that a n n for n 2 . But the inequality a n n does not imply the univalence of f . 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 α ( 0 α < 1 ) for functions with prescribed coefficient bound on the analytic part.


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Om P. Ahuja. Sumit Nagpal. V. Ravichandran. "Radius Constants for Functions with the Prescribed Coefficient Bounds." Abstr. Appl. Anal. 2014 (SI07) 1 - 12, 2014.


Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07022405
MathSciNet: MR3261223
Digital Object Identifier: 10.1155/2014/454152

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI07 • 2014
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