Fixed point results for Geraghty–Ćirić-type contraction mappings in b-metric space with applications

Abstract

Abstract In this study, we manifest a new class of mappings that satisfy Geraghty–Ćirić-type contractive conditions in the context of b-metric spaces and prove a theorem on the existence and uniqueness of fixed points. Our results unify and generalize the results of Geraghty; Ćirić; Dukic, Kadelburg, and Radenović; and Shu-fang Li, Fei Hi, and Ning Lu in the setting of b-metric spaces. Furthermore, we provide examples to verify the correctness and applicability of our results. We also utilize our findings to show the existence of a unique solution for a nonlinear integral equation.

Keywords

• Fixed point
• b-metric spaces
• Geraghty–Ćirić-type contraction
• Nonlinear integral equations