Weak Convergence Theorem by a New Extragradient Method for Fixed Point Problems and Variational Inequality Problems

2014/03/13 by Karahan, Ibrahim, Ozdemir, Murat
#FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1403.3204

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.

Related

• A New Iterative Projection Method for Approximating Fixed Point Problems and Variational Inequality Problems
• Solution of variational inequality problems on fixed point sets of nonexpansive mappings using iterative methods
• Convergence theorems by extragradient method in Banach spaces
• On the strong convergence of a perturbed algorithm to the unique solution of a variational inequality problem
• Strong convergence with a modified iterative projection method for hierarchical fixed point problems and variational inequalities