Viscosity iteration in CAT(k) spaces

TL;DR

This paper investigates the convergence of viscosity iteration algorithms for fixed points of nonexpansive mappings within CAT(k) spaces, demonstrating that the generated sequences reliably approach fixed points based on the contraction used.

Contribution

It extends viscosity iteration methods to CAT(k) spaces, providing convergence results for fixed point approximation in these geometric settings.

Findings

Convergence of viscosity iteration sequences in CAT(k) spaces.

Dependence of the limit fixed point on the contraction parameter.

Extension of fixed point approximation methods to non-Euclidean geometries.

Abstract

We study the approximation of fixed points of nonexpansive mappings in CAT(k) spaces. We show that the iterative sequence generated by the Moudafi's viscosity type algorithm converges to one of the fixed points of the nonexpansive mapping depending on the contraction applied in the algorithm.