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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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