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 (ψ, ϕ) 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 wmappings. 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.

Some Globally Stable Fixed Points in b-Metric Spaces

“…In 2013, Kamihigashi and Stachurski proved some existence and uniqueness theorems of a fixed point in a complete metric space [8]. In 2017, Rezai and Dinarvand [23] established the existence of a fixed point using a setting that generalizes the Chatterjea contraction mapping [16]. Recently in 2018, Yusuf and Kumam [9] extend the work of Kamihigashi and Stachurski to a partial metric space.…”