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.