Common Fixed Points of Asymptotically Regular Mappings in Convex Metric Spaces with Application (European Journal of Pure and Applied Mathematics, 2025)
In this paper, based upon Górnicki's work on fixed points of a continuous asymptotically regular self-mapping on a metric space, we establish common fixed point results for similar self-mappings and their average mappings on a convex metric space by using various types of contractive conditions. The closedness and convexity of the set of fixed points of a non- self- mapping is obtained here in the context of a uniformly convex hyperbolic space. We also apply our findings to solve Volterra type integral equations, demonstrating practical use of our work in mathematical analysis and its related fields.
Keywords: Common fixed point; Gornicki-type contraction mapping; Convex Metric Space; Uniformly Convex Hyperbolic Space; Asymptotically Regular Mapping; Nonlinear Integral Equations