Weak Convergence Theorem by a New Extragradient Method for Fixed Point Problems and Variational Inequality Problems
Year: 2014
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Karahan, Ibrahim, Ozdemir, Murat
Institutions: Erzurum Technical University, Atatürk University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1777051046