Abstract
AbstractRecently, Gordji et al. [Math. Comput. Model. 54, 1897-1906 (2011)] prove the coupled coincidence point theorems for nonlinear contraction mappings satisfying commutative condition in intuitionistic fuzzy normed spaces. The aim of this article is to extend and improve some coupled coincidence point theorems of Gordji et al. Also, we give an example of a nonlinear contraction mapping which is not applied by the results of Gordji et al., but can be applied to our results.2000 MSC: primary 47H10; secondary 54H25; 34B15.
Highlights
The classical Banach’s contraction mapping principle first appear in [1]
In [19], Saadati et al have modified the notion of intuitionistic fuzzy normed spaces (IFNSs) of Saadati and Park [18]
Gordji et al [41] proved some coupled coincidence point theorems for contractive mappings satisfying commutative condition in partially complete IFNSs as follows: Theorem 1.1 (Gordji et al [41])
Summary
The classical Banach’s contraction mapping principle first appear in [1]. Since this principle is a powerful tool in nonlinear analysis, many mathematicians have much contributed to the improvement and generalization of this principle in many ways (see [2,3,4,5,6,7,8,9,10] and others).One of the most interesting is study to other spaces such as probabilistic metric spaces (see [11,12,13,14,15]). In the other hand, coupled fixed points and their applications for binary mappings in partially ordered metric spaces were introduced by Bhaskar and Lakshmikantham [39]. [40] proved some more generalizations of coupled fixed point theorems in partially ordered sets.
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