Weak and strong convergence of inertial algorithms for solving split common fixed point problems

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 assump...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 17
Main Author Chen, Hong-Yi
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 28.01.2021
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Analysis
Applications of Mathematics
Convergence
Demicontractive mappings
Fixed points (mathematics)
Inertial methods
Iterative methods
Linear operators
Mathematics
Mathematics and Statistics
Multiple-set split monotone variational inclusion problem
Nearly contractive mappings
Split common fixed point problems
47H10
Demicontractive mappings
Inertial methods
47H09
Nearly contractive mappings
Split common fixed point problems
47J25
47H06
Multiple-set split monotone variational inclusion problem
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Summary: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.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02556-4