Mann iteration for monotone nonexpansive mappings in ordered CAT(0) space with an application to integral equations

Abstract

Abstract In this paper, we establish some convergence results for a monotone nonexpansive mapping in a CAT(0) $\operatorname{CAT}(0)$ space. We prove the Δ- and strong convergence of the Mann iteration scheme. Further, we provide a numerical example to illustrate the convergence of our iteration scheme, and also, as an application, we discuss the solution of integral equation. Our results extend some of the relevant results.

Keywords

• CAT ( 0 ) $\operatorname{CAT}(0)$ space
• Fixed point
• Δ-convergence
• Monotone nonexpansive mapping