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Monotone generalized nonlinear contractions in partially ordered metric spaces. (English) Zbl 1158.54019
Summary: A concept of \(g\)-monotone mapping is introduced, and some fixed and common fixed point theorems for \(g\)-non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to R. P. Agarwal, M. A. El–Gebeily, and D. O’Regan [Appl. Anal. 87, No. 1, 109–116 (2008; Zbl 1140.47042)].

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
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