Common Fixed Points of Asymptotically Regular Mappings in Convex Metric Spaces with Application

In this paper, based upon G\'{o}rnicki'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.