Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2014 / Cilt: 63 - Sayı: 1
WEAK CONVERGENCE THEOREM BY A NEW EXTRAGRADIENT METHOD FOR FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 43–53
- DOI
- —
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 ...nding a common element of the set of ...xed 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.