Fixed point theorems and iterative approximations for monotone nonexpansive mappings in ordered Banach spaces

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Song Y., Kumam P., Cho Y.J.

Publisher: SpringerOpen

Publication year: 2016

Journal: Fixed Point Theory and Applications (1687-1820)

Volume number: 2016

Issue number: 1

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84977516287&doi=10.1186%2fs13663-016-0563-y&partnerID=40&md5=ef252cd4c96f830e6729a77df77a9feb

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we prove some existence theorems of fixed points of a monotone nonexpansive mapping T in a Banach space E with the partial order ‘≤’, where a such mapping may be discontinuous. In particular, in finite dimensional spaces, such a mapping T has a fixed point in E if and only if the sequence { Tn0 } is bounded in E. In order to find a fixed point of such a mapping T, we prove the weak convergence of the Mann iteration scheme under the condition ∑n=1∞βn(1−βn)=∞, which entails βn=1n+1 as a special case. © 2016, Song et al.

Keywords

Mann iterative scheme, monotone nonexpansive mapping, ordered Banach space, λ-hybrid mapping