Some Fixed Point Results for (β-ψ1-ψ2)-contractive Conditions in Ordered b-metric-like Spaces

Abstract

This paper extends and generalizes the results of paper [Aiman Mukheimer : ($\alpha-\psi-\varphi$)-contractive mappings in ordered partial $b$-metric spaces J. Nonlinear Sci. Appl. {7}, 168--179 (2014)]. Two new concepts of ($\beta$-$\psi_1$-$\psi_2$)-contractive mapping using two altering distance functions in ordered $b$-metric-like space are introduced and study based fixed point results. Counter examples are illustrated to check the applicability and effectiveness of the work. As an application the existence of solution of integral equations is proved.