Convergence of a Tri-Inertial Split-Averaged λ-Iteration Scheme in Cone Banach Spaces (Letters in Nonlinear Analysis and its Applications, 2025)
We introduce a novel multi-inertial λ-iteration scheme in cone Banach spaces, using a tri-Inertial split-averaged λ-iteration process, which we denote as TISA-λ-iteration. Under mild assumptions including quasi-nonexpansiveness, weak contraction, and compatibility of mappings, we establish convergence theorems demonstrating both existence and uniqueness of fixed points. A simple one-dimensional example is used to illustrate theoretically and numerically that the proposed scheme accelerates convergence compared to Krasnoselskii-Mann, and remains competitive with recent two-step inertial frameworks of Cortild–Peypouquet. Our method’s added flexibility allows it to adapt to operator geometry, manage multiple error terms, and encompass prior methods as special cases. We discuss the implications of this flexibility,show visual and quantitative comparisons, and indicate directions for further optimization and experimental validation.
Keywords: Fixed point theory; cone Banach spaces; multi-inertial iteration; weak contraction; Tri-Inertial Split-Averaged λ-Iteration