A New Iterative Projection Method for Approximating Fixed Point Problems and Variational Inequality Problems
Abstract
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an inverse strongly monotone mapping in a real Hilbert space. Also, we prove that under quite mild conditions the iterative sequence defined by our new extragradient method converges strongly to a solution of the fixed point problem for an infinite family of nonexpansive mappings and the classical variational inequality problem. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.
Cite
@article{arxiv.1403.3390,
title = {A New Iterative Projection Method for Approximating Fixed Point Problems and Variational Inequality Problems},
author = {Ibrahim Karahan and Murat Ozdemir},
journal= {arXiv preprint arXiv:1403.3390},
year = {2014}
}
Comments
12 pages. arXiv admin note: substantial text overlap with arXiv:1403.3204