Ergodic-type method for a system of split variational inclusion and fixed point problems in Hilbert spaces
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Authors
Dao-Jun Wen
- College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China.
Yi-An Chen
- College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China.
Ying-Ling Lu
- College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China.
Abstract
In this paper, we introduce an ergodic-type method for solving a system of split variational inclusion and fixed point
problems of a family of nonexpansive mappings with averaged resolvent operator. We prove that the sequence generated by the
proposed algorithm converges strongly to a common element of the set of solutions of a system of split variational inclusion
and the set of fixed points of a family of nonexpansive mappings in Hilbert spaces, from which the minimum norm solution
is deduced as a special case. Moreover, a numerical example is given to illustrate the operational reliability and convergence
of the presented method and results, which may be viewed as a refinement and improvement of the previously known results.
Share and Cite
ISRP Style
Dao-Jun Wen, Yi-An Chen, Ying-Ling Lu, Ergodic-type method for a system of split variational inclusion and fixed point problems in Hilbert spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 3046--3058
AMA Style
Wen Dao-Jun, Chen Yi-An, Lu Ying-Ling, Ergodic-type method for a system of split variational inclusion and fixed point problems in Hilbert spaces. J. Nonlinear Sci. Appl. (2017); 10(6):3046--3058
Chicago/Turabian Style
Wen, Dao-Jun, Chen, Yi-An, Lu, Ying-Ling. "Ergodic-type method for a system of split variational inclusion and fixed point problems in Hilbert spaces." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 3046--3058
Keywords
- Split variational inclusion
- nonexpansive mapping
- ergodic-type iteration
- fixed point
- minimum norm solution.
MSC
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