Fixed Point Theorems of Almost Generalized Contractive Mappings in <i>b</i>-Metric Spaces and an Application to Integral Equation

Abstract

In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. To illustrate our work, we present an application on the existence and uniqueness of a nonlinear quadratic integral problem solution. Moreover, an open problem is presented to enable the scope for future research in this area.

Keywords

• <i>b</i>-metric space
• weak contractions
• fixed point, compatible and weakly compatible mappings
• coupled coincidence point
• nonlinear quadratic integral equations