MiKM: multi-step inertial Krasnosel’skiǐ–Mann algorithm and its applications

Some new iterative algorithms for finding fixed points of nonexpansive mappings

“…Recently, some authors [4,13,15] investigated the inertial KM algorithms by combining KM iterations and inertial techniques. Very recently, Dong et al [14] firstly introduced the multi-step inertial KM iterations (MiKM) and showed the numerical advantage of the MiKM.…”

Multi-Step Inertial Regularized Methods for Hierarchical Variational Inequality Problems Involving Generalized Lipschitzian Mappings

“…On the other hand, in order to accelerate the convergence, the inertial methods have been studied extensively by many scholars [5][6][7][8][9][10][11][12]. One of the important results is the inertial Mann algorithm which is introduced by Maingé [5] in 2007:…”

“…In 2019, Dong et al [7] proposed the multi-step inertial Krasnosel'skiǐ-Mann algorithm for finding a fixed point of a nonexpansive mapping, as follows:…”

“…This algorithm has a weak convergence result under certain conditions. In this paper, motivated by the results of [3,4,7], we construct a multi-step inertial regularized subgradient extragradient method and a multi-step inertial regularized Tseng's extragradient method for solving HVIP (4) in a Hilbert space when F is a generalized Lipschitzian and hemicontinuous mapping (see in Section 2, Definitions 2 and 3). Then, we present two strong convergence theorems and give some numerical experiments to show the effectiveness and feasibility of our new iterative methods.…”

New Inertial Relaxed CQ Algorithms for Solving Split Feasibility Problems in Hilbert Spaces

“…then the sequence x n generated by (11) with step size λ n converges weakly to a point of a solution set of the problem (SFP). For recent results on inertial algorithms (see [17][18][19][20][21][22][23][24]).…”