Weak Convergence Theorem by a New Extragradient Method for Fixed Point Problems and Variational Inequality Problems
Functional Analysis
2014-03-14 v1 Optimization and Control
Abstract
We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality for an inverse strongly monotone mapping in a Hilbert space. Using this process, we prove a weak convergence theorem for the class of nonexpansive mappings in Hilbert spaces. Finally, as an application, we give some theorems by using resolvent operator and strictly pseudocontractive mapping.
Cite
@article{arxiv.1403.3204,
title = {Weak Convergence Theorem by a New Extragradient Method for Fixed Point Problems and Variational Inequality Problems},
author = {Ibrahim Karahan and Murat Ozdemir},
journal= {arXiv preprint arXiv:1403.3204},
year = {2014}
}
Comments
10 pages