Convergence theorems in new generalized type of metric spaces and their applications

Abstract

In the present paper we introduce a new generalized type of metric spaces called the right quasi-metric spaces. We state and prove convergence theorems to a fixed point for any map in these spaces. Finally, we give applications of our results. These results generalize the corresponding results in M. A. Ahmed and F. M. Zeyada (On convergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings, J. Math. Anal. Appl., 274(1), 458–465, 2002.