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Article Citation - WoS: 30Citation - Scopus: 35Discussion of Coupled and Tripled Coincidence Point Theorems for Φ-Contractive Mappings Without the Mixed g-monotone Property(Springer international Publishing Ag, 2014) Karapinar, Erdal; Roldan, Antonio; Shahzad, Naseer; Sintunavarat, WutipholAfter 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.Article Citation - WoS: 11Citation - Scopus: 5A Note on 'n-fixed Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces'(Springer int Publ Ag, 2013) Karapinar, Erdal; Roldan, Antonio; Roldan, Concepcion; Martinez-Moreno, JuanIn this note we prove that a kind of mappings depending on k arguments introduced in (Paknazar et al. in Fixed Point Theory Appl. 2013: 111, 2013) only depend on their first argument. Therefore, results in that paper reduce to the unidimensional case. We also include some commentaries about the different notions of multidimensional fixed point.

