Modified proximal-like extragradient methods for two classes of equilibrium problems in Hilbert spaces with applications

In the literature, the most authors modify the viscosity methods or hybrid projection methods to construct the strong convergence algorithms for solving the pseudomonotone equilibrium problems. In this paper, we introduce some new extragradient methods with non-convex combination to solve the pseudomonotone equilibrium problems in Hilbert space and prove the strong convergence for the constructed algorithms. Our algorithms are very different with the existing ones in the literatures. As the application, the fixed point theorems for strict pseudo-contraction are considered. Finally, some numerical examples are given to show the effectiveness of the algorithms.

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Inertial Extragradient Methods for Solving Split Equilibrium Problems

Mathematics ◽

10.3390/math9161884 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1884

Author(s):

Suthep Suantai ◽

Narin Petrot ◽

Manatchanok Khonchaliew

Keyword(s):

Strong Convergence ◽

Hilbert Spaces ◽

Numerical Experiments ◽

Equilibrium Problems ◽

Constraint Qualifications ◽

Weak And Strong Convergence ◽

Convergence Theorems ◽

Extragradient Methods

This paper presents two inertial extragradient algorithms for finding a solution of split pseudomonotone equilibrium problems in the setting of real Hilbert spaces. The weak and strong convergence theorems of the introduced algorithms are presented under some constraint qualifications of the scalar sequences. The discussions on the numerical experiments are also provided to demonstrate the effectiveness of the proposed algorithms.

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Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications

Demonstratio Mathematica ◽

10.1515/dema-2021-0030 ◽

2021 ◽

Vol 54 (1) ◽

pp. 280-298

Author(s):

Nuttapol Pakkaranang ◽

Habib ur Rehman ◽

Wiyada Kumam

Keyword(s):

Hilbert Space ◽

Hilbert Spaces ◽

Numerical Experiments ◽

Equilibrium Problems ◽

Real Hilbert Space ◽

Type Condition ◽

Step Size ◽

Extragradient Methods ◽

Iterative Schemes ◽

Mild Conditions

Abstract The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The applications of proposed results are studied to solve variational inequalities and fixed point problems in the setting of real Hilbert spaces. Many numerical experiments have been provided in order to show the algorithmic performance of the proposed methods and compare them with the existing ones.

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Extragradient methods with CQ technique for fixed point problems and equilibrium problems

Filomat ◽

10.2298/fil2014783y ◽

2020 ◽

Vol 34 (14) ◽

pp. 4783-4793

Author(s):

Zhangsong Yao ◽

Yeong-Cheng Liou ◽

Li-Jun Zhu

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Hilbert Spaces ◽

Equilibrium Problems ◽

Iterative Algorithms ◽

Convergence Result ◽

Fixed Point Problems ◽

Common Element ◽

Extragradient Methods ◽

Extragradient Algorithm

In this paper, we study iterative algorithms for solving fixed point problems and equilibrium problems in Hilbert spaces. We present an extragradient algorithm with CQ technique for finding a common element of the fixed points of pseudocontractive operators and the solutions of pseudomonotone equilibrium problems. Strong convergence result of the proposed algorithm is proved.

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