Strong convergence theorems for maximal monotone operators and continuous pseudocontractive mappings

Volume 9, Issue 6, pp 4409--4426 http://dx.doi.org/10.22436/jnsa.009.06.81

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Authors

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

Abstract

We introduce a new iterative algorithm for finding a common element of the solution set of the variational inequality problem for a continuous monotone mapping, the zero point set of a maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the sequence generated by the proposed algorithm to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets. As applications, we consider iterative algorithms for the equilibrium problem coupled with fixed point problem.

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Keywords

• Maximal monotone operator
• continuous monotone mapping
• continuous pseudocontractive mapping
• fixed points
• variational inequality
• zeros
• minimum-norm point.

MSC

•  47H05
•  47H09
•  47H10
•  47J05
•  47J20
•  47J25
•  49M05

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