Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized Meir-Keeler Type Contractions

We prove coupled coincidence point and coupled fixed point results of ∶×→ and ∶→ involving Meir-Keeler type contractions on the class of partially ordered metric spaces. Our results generalize some recent results in the literature. Also, we give some illustrative examples and application

Septal perforators stemming from a very long left main coronary artery

We report a case of a very long left main coronary artery, 58mm,  with septal perforators before bifurcation. The coronary arteries were seen clear of plaques. To the best of our knowledge this case is a very rare case because of the existance of the first and the second septal perforator arteries originating from a very long left main coronary artery

Iterative approximation of fixed points of Prešić operators on partial metric spaces

Please read abstract in the article.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616hb2017Mathematics and Applied Mathematic

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