Viscosity Iterative algorithm for solving Variational Inclusion and Fixed point problems involving Multivalued Quasi-Nonexpansive and Demicontractive Operators in real Hilbert Space

TL;DR

This paper introduces a modified viscosity iterative algorithm for solving variational inclusion and fixed point problems involving multi-valued quasi-nonexpansive and demi-contractive operators in Hilbert spaces, ensuring strong convergence.

Contribution

It develops a new viscosity iterative process that combines fixed point and viscosity approximation techniques for improved convergence in complex operator problems.

Findings

Proves strong convergence of the proposed algorithm.

Handles multi-valued quasi-nonexpansive and demi-contractive operators.

Provides a robust method for variational inclusion problems.

Abstract

This paper presents a modified general viscosity iterative process designed to solve variational inclusion and fixed point problems involving multi-valued quasi-nonexpansive and demi-contractive operators. The modified iterative process incorporates a viscosity approximation technique to handle the nonexpansive and contractive mappings, providing a more robust and efficient solution approach. By introducing an additional sequence of iterates, the algorithm iteratively approximates the desired solution by combining fixed point iteration with viscosity approximation. The proposed method has been proven to converge strongly to the solution of the given problem, ensuring the reliability and accuracy of the results.