Coupled fixed point theorems for nonlinear contractions without mixed monotone property

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Publication Details

Author list: Sintunavarat W., Kumam P., Cho Y.J.

Publisher: SpringerOpen

Publication year: 2012

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

Volume number: 2012

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84879829362&doi=10.1186%2f1687-1812-2012-170&partnerID=40&md5=6fbfb80f8180cd5396ca637699735d27

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fixed point of the given mapping. Further, we apply our results to the existence of a coupled fixed point of the given mapping in partially ordered metric spaces. Moreover, some applications to integral equations are presented. ฉ 2012 Sintunavarat et al.; licensee Springer.

Keywords

Coupled fixed point, F-invariant set, Mixed monotone property, Partially ordered set, Transitive property