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  • Research Article
  • Open Access

A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings

Journal of Inequalities and Applications20092009:520301

https://doi.org/10.1155/2009/520301

  • Received: 3 June 2009
  • Accepted: 1 November 2009
  • Published:

Abstract

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.

Keywords

  • Hilbert Space
  • Approximation Method
  • Variational Inequality
  • Convergence Theorem
  • Monotone Mapping

Publisher note

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

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