6 results
Search Results
Now showing 1 - 6 of 6
Article Citation - WoS: 28Citation - Scopus: 33Coincidence Point Theorems in Quasi-Metric Spaces Without Assuming the Mixed Monotone Property and Consequences in g-metric Spaces(Springer international Publishing Ag, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; de la Sen, ManuelIn this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.Article Citation - WoS: 12Citation - Scopus: 21On Some Fixed Point Theorems Under (α, Ψ, Φ)-Contractivity Conditions in Metric Spaces Endowed With Transitive Binary Relations(Springer international Publishing Ag, 2015) Shahzad, Naseer; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoAfter the appearance of Nieto and Rodriguez-Lopez's theorem, the branch of fixed point theory devoted to the setting of partially ordered metric spaces have attracted much attention in the last years, especially when coupled, tripled, quadrupled and, in general, multidimensional fixed points are studied. Almost all papers in this direction have been forced to present two results assuming two different hypotheses: the involved mapping should be continuous or the metric framework should be regular. Both conditions seem to be different in nature because one of them refers to the mapping and the other one is assumed on the ambient space. In this paper, we unify such different conditions in a unique one. By introducing the notion of continuity of a mapping from a metric space into itself depending on a function alpha, which is the case that covers the partially ordered setting, we extend some very recent theorems involving control functions that only must be lower/upper semi-continuous from the right. Finally, we use metric spaces endowed with transitive binary relations rather than partial orders.Article Citation - WoS: 5Citation - Scopus: 4Some remarks on 'Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces'(Springer international Publishing Ag, 2014) Agarwal, Ravi P.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoThe main aim of this paper is to advise researchers in the field of Fixed Point Theory against an extended mistake that can be found in some proofs. We illustrate our claim proving that theorems in the very recent paper (Wang in Fixed Point Theory Appl. 2014: 137, 2014) are incorrect, and we provide different corrected versions of them.Article Citation - WoS: 24Citation - Scopus: 5Remarks on 'Coupled coincidence point results for a generalized compatible pair with applications'(Springer international Publishing Ag, 2014) Erhan, Inci M.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, NaseerVery recently, Hussain et al. (Fixed Point Theory Appl. 2014:62, 2014) announced the existence and uniqueness of some coupled coincidence point. In this short note we remark that the announced results can be derived from the coincidence point results in the literature.Article Citation - WoS: 3Citation - Scopus: 4A Short-Note on 'common Fixed Point Theorems for Non-Compatible Self-Maps in Generalized Metric Spaces'(Springer international Publishing Ag, 2015) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Alsulami, Hamed H.The main aim of this short-note is point out that certain hypotheses assumed on some results in the very recent paper (Yang in J. Inequal. Appl. 2014:275, 2014) are unnecessary, and the results contained in that manuscript can easily be improved.Article Citation - WoS: 1Citation - Scopus: 2On an Extension of Contractivity Conditions Via Auxiliary Functions(Springer international Publishing Ag, 2015) Agarwal, Ravi P.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-FranciscoIn this manuscript, we study sufficient conditions on the functions that appears in very complex contractivity conditions introduced in a recent manuscript by Liu et al. in order to guarantee the existence and uniqueness of common fixed points of four self-mappings.
