On viscosity iterative methods for variational inequalities

By Yonghong Yao, Muhammad Aslam Noor. 2007

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Abstract Let J ˜ be a commutative family of nonexpansive mappings of a closed convex subset C of a reflexive Banach space X such that the set of common fixed point is nonempty. In this paper, we suggest and analyze a new viscosity iterative method for a commutative family of nonexpansive mappings. We also prove that the approximate solution obtained by the proposed method converges to a solution of a variational inequality. Our method of proof is simple and different from the other methods. Results proved in this paper may be viewed as an improvement and refinement of the previously known results.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4f91f16efbdd0374308745436894be4dfcecc07c

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In Computational Theory and Mathematics

In Geometry and Topology

In Numerical Analysis

Citations in the corpus

Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces (2010, methodology): “For the physical formulation, applications, numerical methods and other aspects of the variational inequalities, see [17–28] and the references therein.”