On a cyclic Jungck modified TS-iterative procedure with application examples

This article investigates some properties of quasi-cyclic and cyclic Jungck modified TS-iterative schemes in complete metric spaces and Banach spaces. In particular, properties of convergence of distances and sequences associated with the self-mappings which define the Jungck modified TS-iterative procedures are studied as well as some properties concerning the convergence of the solution to common fixed points or best proximity points of both self-mappings. The uniqueness of the best proximity points is investigated. It is basically assumed that one of the self-mappings is asymptotically nonexpansive while the other is asymptotically contractive with several particular cases. Some application examples are also discussed.