Accelerated Krasnosel'skiĭ–Mann iteration via convex combination and inertial techniques
Fixed Point Methods and Optimization, Volume 3, Issue 2, August 2026, Pages 138–146
FANGBING LV
College of Science, Civil Aviation University of China, Tianjin 300300, China
FENGJING MO
College of Science, Civil Aviation University of China, Tianjin 300300, China
Abstract
In this article, we introduce an accelerated Krasnosel'skiĭ-Mann--Mann iteration for finding a fixed point of a nonexpansive mapping in Hilbert spaces, which combines Krasnosel'skiĭ-Mann--Mann iteration with convex combination and inertial techniques. The weak convergence of the proposed method is established. Finally, we give preliminary experiments to illustrate the advantage of the accelerated Krasnosel'skiĭ-Mann--Mann method.
Cite this Article as
Fangbing Lv and Fengjing Mo, Accelerated Krasnosel'skiĭ–Mann iteration via convex combination and inertial techniques, Fixed Point Methods and Optimization, 3(2), 138–146, 2026