On a subclass of p-harmonic mappings

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Published: Sep 30, 2013
DOI: https://doi.org/10.5556/j.tkjm.44.2013.1053
Keywords:
Harmonic Univalent functions extreme points

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Saurabh Porwal
Kaushal Kishore Dixit

Abstract

The purpose of the present paper is to introduce two new classes $HS_p(\alpha)$ and $HC_p(\alpha)$ of $p$-harmonic mappings together with their corresponding subclasses $HS^0_p(\alpha)$ and $HC^0_p(\alpha)$. We prove that the mappings in $HS_p(\alpha)$ and $HC_p(\alpha)$ are univalent and sense-preserving in $U$ and obtain extreme points of $HS^0_p(\alpha)$ and $HC^0_p(\alpha)$, $HS_p(\alpha)\cap T_p$ and $HC_p(\alpha)\cap T_p$ are determined, where $T_p$ denotes the set of $p$-harmonic mapping with non negative coefficients. Finally, we establish the existence of the neighborhoods of mappings in $HC_p(\alpha)$. Relevant connections of the results presented here with various known results are briefly indicated.

Article Details

How to Cite
Porwal, S., & Dixit, K. K. (2013). On a subclass of p-harmonic mappings. Tamkang Journal of Mathematics, 44(3), 313–325. https://doi.org/10.5556/j.tkjm.44.2013.1053
Issue
Vol. 44 No. 3 (2013)
Section
Papers
Author Biographies

Saurabh Porwal

Department ofMathematics, U.I.E.T. Campus, C.S.J.M. University, Kanpur-208024, (U.P.), India.

Kaushal Kishore Dixit

Department of Engineering Mathematics, Gwalior Institute of Information Technology, Gwalior-474015, (M.P.),India.

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