Fixed Point Methods and Optimization

Electronic ISSN: 3008-1548

DOI: 10.69829/fpmo

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