Global Conference on Mathematics and Applications (GCMA)

In this paper, we study fixed point results for $\varphi$-contractions on complete $b$-metric spaces. Under suitable assumptions on the comparison function $\varphi$, we establish two types of estimates for the convergence rate of the corresponding Picard iterative sequence. The obtained results are subsequently applied to Urysohn integral equations in the space of continuous functions equipped with an appropriate $(b)$-metric. By imposing suitable contractive conditions on the nonlinear term, we establish the existence and uniqueness of solutions. Finally, an illustrative example is provided to demonstrate the applicability of the theoretical results and to obtain explicit estimates for the convergence rate of the associated iterative process.