An Iterative Approach to Common Fixed Points of G-Nonexpansive Mappings with Applications in Solving the Heat Equation

Abstract

This study presents an iterative method for approximating common fixed points of a finite set of G-nonexpansive mappings within a real Hilbert space with a directed graph. We establish definitions for left and right coordinate convexity and demonstrate both weak and strong convergence results based on reasonable assumptions. Furthermore, our algorithm’s effectiveness in solving the heat equation is highlighted, contributing to energy optimization and sustainable development.

Keywords

• fixed point problem
• G-nonexpansive mapping
• parallel method
• process innovation