Outer approximation method for constrained composite fixed point problems involving Lipschitz pseudo contractive operators

TL;DR

This paper introduces an outer approximation iterative method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators, with proven convergence and applications to various problems.

Contribution

It presents a novel outer approximation method that handles complex operator compositions in Hilbert spaces, extending existing fixed point algorithms.

Findings

Method converges under specified conditions.

Applicable to monotone inclusion splitting.

Demonstrated effectiveness on constrained equilibrium problems.

Abstract

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these operators and an outer approximation given by the projection onto a closed half-space containing the constraint set. Its convergence is established and applications to monotone inclusion splitting and constrained equilibrium problems are demonstrated.