A Unified Version of Ran and Reuring’s Theorem and Nieto and Rodr?guez-L?pez’s Theorem and Low-Dimensional Generalizations

Authors

Antonio-Francisco Rold?n-L?pez-de-Hierro, Department of Quantitative Methods for Economics and Business, University of Granada, Granada, SpainFollow

Author Country (or Countries)

Spain

Abstract

In this paper, we show the very close relationship between two of the pioneering theorems on fixed point theory in partially ordered metric spaces, such us Ran and Reuring’s theorem and Nieto and Rodr´ıguez-L´opez’s theorem. Although they seem to be independent, they are both two faces of an unified result. Furthermore, we extend the kind of control functions involved in the contractivity condition and we use preorders rather than partial orders, which have the main advantage of unify, in a same condition, two usual cases: the framework in which none binary relation is considered and the partially ordered case.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/100201

Recommended Citation

Rold?n-L?pez-de-Hierro, Antonio-Francisco (2016) "A Unified Version of Ran and Reuring’s Theorem and Nieto and Rodr?guez-L?pez’s Theorem and Low-Dimensional Generalizations," Applied Mathematics & Information Sciences: Vol. 10: Iss. 2, Article 1.
DOI: http://dx.doi.org/10.18576/amis/100201
Available at: https://digitalcommons.aaru.edu.jo/amis/vol10/iss2/1