Radius Constants for Functions with the Prescribed Coefficient Bounds

Om P. Ahuja, Sumit Nagpal and V. Ravichandran

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: For an analytic univalent function f(z)=z+∑n=2∞anzn in the unit disk, it is well‐known that |an| ≤ n for n ≥ 2. But the inequality |an| ≤ 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

Date: 2014
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https://doi.org/10.1155/2014/454152

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:454152

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