Iterative Methods for Common Fixed Points of a Finite Family of Non-self Mappings

In memoriam Professor Charles E. Chidume (1947–2021)

Abstract

In this paper, iterative processes involving a finite family  of non-self mappings defined on a nonempty closed convex subset of a complete CAT(0) space are constructed. Some strong convergence and $\triangle$-convergence results for approximating common fixed points of a finite family of $k$-strictly pseudocontractive mappings are obtained. In addition, strong convergence results for approximating a common fixed point of a finite family of demicontractive non-self mappings are obtained under some appropriate conditions. The results obtained in this paper improve, generalize and complement  many of the results in the literature.