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A Unified Version of Ran and Reuring�s Theorem and Nieto and Rodr�guez-L�pez�s Theorem and Low-Dimensional Generalizations |
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PP: 383-393 |
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doi:10.18576/amis/100201
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Author(s) |
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Antonio-Francisco Rold�n-L�pez-de-Hierro,
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Abstract |
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| 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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