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Common fixed points of a generalized ordered \(g\)-quasicontraction in partially ordered metric spaces. (English) Zbl 1286.54048
Summary: The concept of a generalized ordered \(g\)-quasicontraction is introduced, and some fixed and common fixed point theorems for a \(g\)-nondecreasing generalized ordered \(g\)-quasicontraction mapping in partially ordered complete metric spaces are proved. We also show the uniqueness of the common fixed point in the case of a generalized ordered \(g\)-quasicontraction mapping. Finally, we prove fixed point theorems for mappings satisfying the so-called weak contractive conditions in the setting of a partially ordered metric space. The presented theorems are generalizations of very recent fixed point theorems due to Z. Golubović et al. [Fixed Point Theory Appl. 2012, Article ID 20 (2012; Zbl 1273.54055)].

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces
54F05 Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
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