Radius Constants for Functions with the Prescribed Coefficient Bounds

Abstract EN

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<1) for functions with prescribed coefficient bound on the analytic part.