Annals of Mathematical Sciences and Applications

Volume 7 (2022)

Number 2

Weak convergence of two-step inertial iteration for countable family of quasi-nonexpansive mappings

Pages: 259 – 279



Yekini Shehu (College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, China)

Jen-Chih Yao (Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan)


In this paper, we propose and study an iterative method with two-step inertial extrapolation to find a common fixed point of countable family of certain quasi-nonexpansive mappings in real Hilbert spaces. We obtain weak convergence analysis of the proposed method under some standard conditions. Our results unify and extend several inertial-type methods already appeared in the literature.


two-point inertia, weak convergence, quasi-nonexpansive mappings, Hilbert spaces

2010 Mathematics Subject Classification

49M25, 68Q25, 90C22, 90C25, 90C30, 90C60

Received 21 July 2022

Accepted 21 July 2022

Published 12 September 2022