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A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings
Journal of Inequalities and Applications volume 2009, Article number: 520301 (2009)
A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.
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Klin-eam, C., Suantai, S. A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings. J Inequal Appl 2009, 520301 (2009). https://doi.org/10.1155/2009/520301
- Hilbert Space
- Approximation Method
- Variational Inequality
- Convergence Theorem
- Monotone Mapping