Journal of Nonlinear Analysis and Application

Volume 2018, No. 1 (2018), Pages 34-47

Article ID jnaa-00367, 14 Pages

doi: 10.5899/2018/jnaa-00367


Research Article


Hybrid fixed point in CAT(0) spaces


Hemant Kumar Pathak1, Ismat Beg2 *


1Pt. Ravishankar Shukla University Raipur (C.G.), 492010, India

2Lahore School of Economics, Lahore 53200, Pakistan


* Corresponding author. Email address: ibeg@lahoreschool.edu.pk


Received: 15 January 2017; Accepted: 07 July 2017


Copyright © 2018 Hemant Kumar Pathak and Ismat Beg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we introduce an ultrapower approach to prove fixed point theorems for H^{+}-nonexpansive multi-valued mappings in the setting of CAT(0) spaces and prove several hybrid fixed point results in CAT(0) spaces for families of single-valued nonexpansive or quasinonexpansive mappings and multi-valued upper semicontinuous, almost lower semicontinuous or H^{+}-nonexpansive mappings which are weakly commuting. We also establish a result about structure of the set of fixed points of H^{+}-quasinonexpansive mapping on a CAT(0) space.


Keywords: Fixed point; H^{+}-nonexpansive mapping; H^{+}-quasinonexpansive mapping; demiclosed; CAT(0) space; proximinal set.


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