Abstract
Abstract In this paper, we prove some coupled coincidence point theorems in fuzzy normed spaces. Our results improve and restate the proof lines of the main results given in the papers (Eshaghi Gordji et al. in Math. Comput. Model. 54:1897-1906, 2011) and (Sintunavarat et al. in Fixed Point Theory Appl. 2011:81, 2011). MSC:47H10, 54H25, 34B15.
Highlights
1 Introduction Recently, many authors have shown the existence of coupled fixed points and common fixed points for some contractions in cone metric spaces, partially ordered metric spaces, fuzzy metric spaces, fuzzy normed spaces, intuitionistic fuzzy normed spaces and others ([ – ])
In [ ], Sintunavarat et al proved some coupled fixed point theorems for contractive mappings in partially complete intuitionistic fuzzy normed spaces, which extended and improved coupled coincidence point theorems in Gordji et al [ ]
The authors found some mistakes in the proof lines of the main result (Theorem . ) of [ ] and the same mistakes in [ ]
Summary
Many authors have shown the existence of coupled fixed points and common fixed points for some contractions in cone metric spaces, partially ordered metric spaces, fuzzy metric spaces, fuzzy normed spaces, intuitionistic fuzzy normed spaces and others ([ – ]).Especially in [ ], Sintunavarat et al proved some coupled fixed point theorems for contractive mappings in partially complete intuitionistic fuzzy normed spaces, which extended and improved coupled coincidence point theorems in Gordji et al [ ]. ( ) If (X, ) is a partially ordered set, X is said to have the sequential g-monotone property if it verifies the following properties: (B ) If {xn} is a non-decreasing sequence and limn→∞ xn = x, gxn gx for all n ∈ N.
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