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.
"Radius Constants for Functions with the Prescribed Coefficient Bounds." Abstr. Appl. Anal. 2014 (SI07) 1 - 12, 2014. https://doi.org/10.1155/2014/454152