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Common fixed points of ordered \(g\)-contractions in partially ordered metric spaces. (English) Zbl 1345.54060
Summary: The concept of ordered \(g\)-contraction is introduced, and some fixed and common fixed point theorems for \(g\)-nondecreasing ordered \(g\)-contraction mapping in partially ordered metric spaces are proved. We also show the uniqueness of the common fixed point in the case of an ordered \(g\)-contraction mapping. The theorems presented are generalizations of very recent fixed point theorems due to Z. Golubović et al. [Fixed Point Theory Appl. 2012, Article ID 20, 11 p. (2012; Zbl 1273.54055)].

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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