Common fixed points of ordered \(g\)-contractions in partially ordered metric spaces.

*(English)*Zbl 1345.54060Summary: 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 |

##### Keywords:

ordered \(g\)-contraction; \(g\)-nondecreasing; common fixed point; coincidence fixed point; partially ordered metric spaces
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\textit{X.-l. Liu}, Fixed Point Theory Appl. 2014, Paper No. 28, 19 p. (2014; Zbl 1345.54060)

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