Strong convergence of some iterative algorithms for a general system of variational inequalities

Volume 10, Issue 7, pp 3887--3902 http://dx.doi.org/10.22436/jnsa.010.07.42

Publication Date: July 27, 2017 Submission Date: April 19, 2017

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Authors

Jong Soo Jung - Department of Mathematics, Dong-A University, Busan 49315, Korea.

Abstract

In this paper, we introduce two iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of a general system of variational inequalities for continuous monotone mappings and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Then we establish strong convergence of the sequence generated by the proposed iterative algorithms to a common element of the solution set and the fixed point set, which is the unique solution of a certain variational inequality.

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Keywords

• Composite iterative algorithm
• general system of variational inequatlites
• continuous monotone mapping
• continuous peudocontractive mapping
• \(\rho\)-Lipschitzian
• \(\eta\)-strongly monotone mapping
• variational inequality
• strongly positive bounded linear operator
• fixed points.

MSC

•  47J20
•  47H05
•  47H09
•  47H10
•  49J40
•  49M05

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