Fixed Point Results in Convex Double-Controlled Metric-Type Spaces and Applications

This paper investigates fixed point results in convex double-controlled metric-type spaces. By introducing a convex structure on double-controlled metric-type spaces, we study the convergence of the Mann iteration process for contractive mappings in this framework. Under suitable conditions on the control functions, we establish the existence and uniqueness of fixed points and prove that the Mann iterative sequence converges to the fixed point. In addition, we investigate the stability of the Mann iteration process and establish a data dependence result. Finally, an application to a Fredholm integral equation is presented to illustrate the applicability of the obtained results.