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Common fixed points for nonlinear \((\psi ,\phi)_{s}\)-weakly \(C\)-contractive mappings in partially ordered \(b\)-metric spaces. (English) Zbl 1453.54019

Summary: In this paper, we introduce the concept of \((\psi ,\phi)_{s}\)-weakly \(C\)-contractive mappings in the setup of partially ordered \(b\)-metric spaces and investigate some fixed point and common fixed point results for such mappings. Our main results generalize several well-known comparable results in the recent literature. Furthermore, we furnish some suitable examples and an applications of a common solution for a system of integral equations to illustrate the effectiveness and usability of our obtained 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
54E50 Complete metric spaces
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