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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 10 > No. 2


A Unified Version of Ran and Reuring’s Theorem and Nieto and Rodríguez-López’s Theorem and Low-Dimensional Generalizations

PP: 383-393
Antonio-Francisco Roldán-López-de-Hierro,
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.

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