On De la Vallée Poussin means for harmonic mappings

dc.contributor.author	Kaliraj, A.S.
dc.date.accessioned	2022-07-17T10:01:23Z
dc.date.available	2022-07-17T10:01:23Z
dc.date.issued	2022-07-17
dc.identifier.uri	http://localhost:8080/xmlui/handle/123456789/3671
dc.description.abstract	In this article, we study the geometric properties of Vn(f), the nth De la Vallée Poussin means for univalent starlike harmonic mappings f. In particular, we provide a necessary and sufficient condition for Vn(f) to be univalent and starlike in the unit disk D, when f∈S∗H, the class of all normalized univalent starlike harmonic mappings in D. We determine the radius of fully starlikeness (respectively, fully convexity) of V2(f), when f∈S0H and the result is sharp. Then, we determine the radius rn∈(0,1) so that Vn(f) is univalent and fully starlike in \|z\|<rn, whenever f is univalent and fully starlike harmonic mapping in D. We also discuss about the geometry preserving nature of Vn(f), when f belongs to some well known geometric subclasses of SH.	en_US
dc.language.iso	en_US	en_US
dc.subject	De la Vallée Poussin means	en_US
dc.subject	Univalent harmonic polynomial	en_US
dc.subject	Starlike	en_US
dc.subject	Convex	en_US
dc.subject	Partial sums	en_US
dc.title	On De la Vallée Poussin means for harmonic mappings	en_US
dc.type	Article	en_US