Abstract
Abstract In this paper we present the notion of F-closed set (which is weaker than the concept of F-invariant set introduced in Samet and Vetro (Ann. Funct. Anal. 1:46-56, 2010), and we prove some coupled fixed point theorems without the condition of mixed monotone property. Furthermore, we interpret the transitive property as a partial preorder and, then, some results in that paper and in Sintunavarat et al. (Fixed Point Theory Appl. 2012:170, 2012) can be reduced to the unidimensional case. MSC:46T99, 47H10, 47H09, 54H25.
Highlights
One of the very popular tools of a fixed point theory is the Banach contraction principle which first appeared in
One of the most attractive research topics in fixed point theory is to prove the existence of a fixed point on metric spaces endowed with partial orders
An initial result in this direction was given by Turinici [ ] in. Following this line of research, Ran and Reurings [ ] used a partial order on the ambient metric space to introduce a slightly different contractivity condition, which must be only verified by comparable points
Summary
One of the very popular tools of a fixed point theory is the Banach contraction principle which first appeared in. In , Ran and Reurings proved the following version of the Banach theorem applicable to metric spaces endowed with a partial order. Theorem (Ran and Reurings [ ]) Let (X, ) be an ordered set endowed with a metric d, and let T : X → X be a given mapping.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
