124 research outputs found
Fixed-point theorems for mappings satisfying the ordered contractive condition on noncommutative spaces
Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces
On some fixed point theorems under (α,ψ,ϕ) -contractivity conditions in metric spaces endowed with transitive binary relations
After the appearance of Nieto and Rodríguez-López’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 α, 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.This article was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah. N Shahzad acknowledges with thanks DSR for financial support. A-F Roldán-López-de-Hierro is grateful to the Department of Quantitative Methods for Economics and Business of the University of Granada. The same author has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE
Coupled common fixed point theorems for generalized nonlinear contraction mappings with the mixed monotone property in partially ordered metric spaces
Enriching some recent coincidence theorems for nonlinear contractions in ordered metric spaces
Simple fixed point results for order-preserving self-maps and applications to nonlinear Markov operators
Some unique fixed point theorems for rational contractions in partially ordered metric spaces
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