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The subgradient extragradient method for approximation of fixed-point problem and modification of equilibrium problem
Author(s)
Saechou, Kanyanee
Date Issued
January 1, 2023
Type
Article
Abstract
In this paper, we consider the modification of equilibrium problem (MEP) and new subgradient extragradient algorithm by using the concept of the set of solutions of the modified variational inequality problem introduced by [Kangtunyakarn A. A new iterative scheme for fixed-point problems of infinite family of (Formula presented.) pseudo contractive mappings, equilibrium problem, variational inequality problems. J Optim Theory Appl. 2013;56:1543–1562.]. Then, we establish and prove weak and strong convergence theorem of the new subgradient extragradient algorithm for finding a common element of the set of solutions of the MEP and two sets of the variational inequality problems under some suitable conditions on (Formula presented.) and (Formula presented.) with (Formula presented.). Moreover, we apply our main theorem to prove weak and strong convergence theorems to solve the generalized equilibrium problem, the system of equilibrium problem, the variational inequality problem and the general system of variational inequality problems. Finally, we give two numerical examples to support our main result.
Citation
Optimization, 72(2), 383-410, 2023