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Mathematics 2019, 7(2), 123; https://doi.org/10.3390/math7020123

Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems

1,†
and
2,*,†
1
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2
School of Mathematics and Statistics, Linyi University, Linyi 276000, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 17 December 2018 / Revised: 18 January 2019 / Accepted: 21 January 2019 / Published: 24 January 2019
Full-Text   |   PDF [741 KB, uploaded 24 January 2019]

Abstract

The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of infinite dimensional Hilbert spaces. Convergence theorem of the sequences generated in our proposed implicit algorithm is obtained under some weak assumptions. View Full-Text
Keywords: split variational inclusion; fixed-point problem; hierarchical optimization problem; nonexpansive mapping; implicit general iterative method split variational inclusion; fixed-point problem; hierarchical optimization problem; nonexpansive mapping; implicit general iterative method
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ceng, L.-C.; Yuan, Q. Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems. Mathematics 2019, 7, 123.

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