Approximation Theorems for $\mathcal{G}$-nonexpansive Mappings in Hyperbolic Spaces by Using Two-step Iterations

Annual Meeting in Mathematics 2024

Abstract

This article aims to approximate the results of $\mathcal{G}$-nonexpansive mappings for two-step iterations in a hyperbolic space with a directed graph. We prove $\Delta$-convergence as well as strong convergence theorems for such mappings in a hyperbolic space with the directed graph. To support our main results, we perform numerical examples and convergence comparisons of the Picard-Mann hybrid iteration with the Ishikawa iteration process, the modified S-iteration process, and the Thianwan iteration process. The proposed algorithm has been implemented and tested via numerical simulation in MATLAB. The simulation results show that the algorithm converges to the optimal configurations and show the effectiveness of the proposed algorithm.