Common Fixed Points for Nonlinear $(\psi ,\varphi)_{s}$-weakly $C$-contractive Mappings in Partially Ordered $b$-metric Spaces

Abstract

In this paper, we introduce the concept of $(\psi ,\varphi)_{s}$-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.