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Some coincidence point results for generalized $$(\psi,\varphi)$$-weakly contractions in ordered $$b$$-metric spaces. (English) Zbl 1347.54106
Summary: In this paper we present some coincidence point results for four mappings satisfying generalized $$(\psi,\varphi)$$-weakly contractive condition in the framework of ordered $$b$$-metric spaces. Our results extend, generalize, unify, enrich, and complement recently results of H. K. Nashine and B. Samet [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2201–2209 (2011; Zbl 1208.41014)] and W. Shatanawi and B. Samet [Comput. Math. Appl. 62, No. 8, 3204–3214 (2011; Zbl 1232.54041)]. As an application of our results, periodic points of weakly contractive mappings are obtained. Also, an example is given to support our results.

##### 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
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