On the multilevel nonlinear problem and its convergence algorithms

Volume 9, Issue 3, pp 906--919 http://dx.doi.org/10.22436/jnsa.009.03.20

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Authors

Zhenhua He - Department of Mathematics, Tongji University, Shanghai 200092, P. R. China. - Department of Mathematics, Honghe University, Yunnan, 661199, China. Jitao Sun - Department of Mathematics, Honghe University, Yunnan, 661199, China.

Abstract

In this paper, applying the geometrical knowledge of Hilbert spaces, we investigate and analyze a system of multilevel split fixed point problems (MSFP). New split solution algorithms are introduced and strong convergence theorems for (MSFP) are established. At the end of this paper, as an application of our results, we investigate and analyze a system of multilevel split variational inclusion problems (MSVIP) and some strong convergence solution for (MSVIP) are obtained. These results obtained by this paper improve and develop some known ones in the literature.

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Keywords

• Multilevel nonlinear problem
• nonexpansive mapping
• variational inclusion problem
• split solution algorithm
• strong convergence theorem.

MSC

•  47H04
•  47H07
•  47H09
•  47H10
•  47J25

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