Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property

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Publication Details

Author list: Agarwal R.P., Sintunavarat W., Kumam P.

Publisher: SpringerOpen

Publication year: 2013

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

Volume number: 2013

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84897667267&doi=10.1186%2f1687-1812-2013-22&partnerID=40&md5=19d2c8a3c7e0279d10ffa9cf609832d7

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we prove the coupled coincidence point theorems for a w*-compatible mapping in partially ordered cone metric spaces over a solid cone without the mixed g-monotone property. In the case of a totally ordered space, these results are automatically obvious under the assumption given. Therefore, these results can be applied in a much wider class of problems. We also prove the uniqueness of a common coupled fixed point in this setup and give some example which is not applied to the existence of a common coupled fixed point by using the mixed g-monotone property but can be applied to our results. ฉ 2013 Agarwal et al.; licensee Springer.

Keywords

Common coupled fixed point, Cone metric spaces