Abstract
In this paper, we propose two iterative schemes for approximating solutions of split common fixed point problems in multiple linear operators case. The first algorithm implements the Krasnosel’skiĭ–Mann iteration with an inertial effect for which the weak convergence is established under mild assumptions. With the tool of nearly contractive mappings, we introduce a viscosity-type iteration which ensures strong convergence. We apply our results to solve a multiple split monotone variational inclusion problem. A numerical example is given to demonstrate the efficiency of the proposed algorithms.
Highlights
Throughout this paper, let H, K1, K2, . . . , Kr be real Hilbert spaces
Given a not necessarily linear operator T from H into H, we denote by Fix(T) := {x ∈ H | x = Tx} the set of all fixed points of T
As in the common case that incorporating the inertial method in an algorithm greatly improves the performance numerically
Summary
Throughout this paper, let H, K1, K2, . . . , Kr be real Hilbert spaces. Given a not necessarily linear operator T from H into H, we denote by Fix(T) := {x ∈ H | x = Tx} the set of all fixed points of T. Find a point x ∈ Fix(U) such that Ax ∈ Fix(T), Chen Journal of Inequalities and Applications (2021) 2021:26 which was first introduced by Censor and Segal [12] They considered the case of directed operators U and T. As in the common case that incorporating the inertial method in an algorithm greatly improves the performance numerically. Lemma 2.2 ([21]) If T : H → H is β-demicontractive, the fixed point set Fix(T) of T is closed and convex. Lemma 2.4 ([25]) Let H be a Hilbert space and {xn} a sequence in H such that there exists a nonempty set D of H satisfying:.
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