An inertial extragradient algorithm for split problems in Hilbert spaces
- 30 September 2022
- journal article
- research article
- Published by Walter de Gruyter GmbH in Analysis
- Vol. 43 (2), 89-103
- https://doi.org/10.1515/anly-2022-1054
Abstract
In this study, we propose an inertial extragradient algorithm for solving a split generalized equilibrium problem as well as a split feasibility and common fixed point problem. We demonstrate that, under certain reasonable assumptions, the sequences induced by the proposed algorithm converge strongly to a solution of the corresponding problem. In addition, with the help of a numerical example, we demonstrate the efficiency of proposed algorithm. As a result of this paper, some recent well-known results in this area have been improved, generalized, and extended.Keywords
This publication has 22 references indexed in Scilit:
- On a System of Generalized Mixed Equilibrium Problems Involving Variational-Like Inequalities in Banach Spaces: Existence and Algorithmic AspectsAdvances in Operations Research, 2012
- Algorithms for the Split Variational Inequality ProblemNumerical Algorithms, 2011
- Split Monotone Variational InclusionsJournal of Optimization Theory and Applications, 2011
- Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spacesInverse Problems, 2010
- Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert spaceNonlinear Analysis, 2008
- A hybrid iterative scheme for mixed equilibrium problems and fixed point problemsJournal of Computational and Applied Mathematics, 2008
- Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach spaceNonlinear Analysis, 2007
- Iterative oblique projection onto convex sets and the split feasibility problemInverse Problems, 2002
- A multiprojection algorithm using Bregman projections in a product spaceNumerical Algorithms, 1994
- Some methods of speeding up the convergence of iteration methodsUSSR Computational Mathematics and Mathematical Physics, 1964