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On \((\psi ,\varphi )\)-weakly contractive condition in partially ordered metric spaces. (English) Zbl 1232.54041
Summary: Recently, H. K. Nashine and the second author [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2201–2209 (2011; Zbl 1208.41014)] studied some coincidence fixed point and common fixed point theorems for two mappings satisfying \((\psi ,\varphi )\)-weakly contractive condition in an ordered complete metric space. In the present paper, we study some coincidence fixed point and common fixed point theorems for three mappings \(S\), \(T\) and \(R\) satisfying the \((\psi ,\varphi )\)-weakly contractive condition in an ordered complete metric space, where the mappings \(S\) and \(T\) are assumed to be weakly increasing with respect to \(R\). Our results generalize several well-known results in the literature.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
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