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

Izhar Uddin; Chanchal Garodia; Juan Jose Nieto

doi:10.1186/s13660-018-1925-2

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

J Inequal Appl. 2018;2018(1):339. doi: 10.1186/s13660-018-1925-2. Epub 2018 Dec 11.

Authors

Izhar Uddin¹, Chanchal Garodia¹, Juan Jose Nieto²

Affiliations

¹ 1Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi, India.
² 2Departamento de Estadística, Análisis Matemático y Optimización, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela, Spain.

Abstract

In this paper, we establish some convergence results for a monotone nonexpansive mapping in a $CAT (0)$ 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 ) space; Fixed point; Monotone nonexpansive mapping; Δ-convergence.