Discussion of Coupled and Tripled Coincidence Point Theorems for Φ-Contractive Mappings Without the Mixed <i>g</I>-monotone Property
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Date
2014
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Springer international Publishing Ag
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Abstract
After the appearance of Ran and Reuring's theorem and Nieto and Rodriguez-Lopez's theorem, the field of fixed point theory applied to partially ordered metric spaces has attracted much attention. Coupled, tripled, quadrupled and multidimensional fixed point results has been presented in recent times. One of the most important hypotheses of these theorems was the mixed monotone property. The notion of invariant set was introduced in order to avoid the condition of mixed monotone property, and many statements have been proved using these hypotheses. In this paper we show that the invariant condition, together with transitivity, lets us to prove in many occasions similar theorems to which were introduced using the mixed monotone property.
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Roldán López de Hierro, Antonio Francisco/0000-0002-6956-4328; KARAPINAR, ERDAL/0000-0002-6798-3254; Sintunavarat, Wutiphol/0000-0002-0932-1332
Keywords
partially ordered set, fixed point, contractive mapping, mixed monotone property, F-invariant set