New convergent Krasnoselskii-Mann and Halpern-type iterations for fixed point problems
Fixed Point Methods and Optimization, Volume 2, Issue 3, December 2025, Pages 210–219
GRACE NNENNAYA OGWO
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, People’s Republic of China
OLANIYI S. IYIOLA
Department of Mathematics, Morgan State University, Baltimore, MD, USA
YEKINI SHEHU
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, People’s Republic of China
Abstract
In this paper, we introduce two novel iterative algorithms to overcome key limitations in fixed-point theory for nonexpansive mappings in Hilbert spaces. The first algorithm, based on a Krasnoselskii–Mann–type scheme, generates weakly convergent sequences for a nonexpansive mapping under standard conditions. The second algorithm, inspired by the Halpern iteration, is designed to strongly converge to a fixed point of a nonexpansive mapping. Our contributions offer more flexible and broadly applicable tools for solving fixed-point problems in nonlinear analysis and optimization.
Cite this Article as
Grace Nnennaya Ogwo, Olaniyi S. Iyiola and Yekini Shehu, New convergent Krasnoselskii-Mann and Halpern-type iterations for fixed point problems, Fixed Point Methods and Optimization, 2(3), 210–219, 2025