Explicit Halpern-type iterative algorithm for solving equilibrium problems with applications

Volume 25, Issue 2, pp 115--132 http://dx.doi.org/10.22436/jmcs.025.02.02

Publication Date: May 26, 2021 Submission Date: November 08, 2020 Revision Date: January 29, 2021 Accteptance Date: April 15, 2021

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Authors

Kanikar Muangchoo - Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon (RMUTP), 1381 Pracharat 1 Road, Wongsawang, Bang Sue, Bangkok 10800, Thailand.

Abstract

A number of iterative algorithms have been established to solve equilibrium problems, and one of the most effective methods is a two-step extragradient method. The main objective of this study is to introduce a modified algorithm that is constructed around two methods; Halpern-type method and extragradient method with a new size rule to solve the equilibrium problems accompanied with pseudo-monotone and Lipschitz-type continuous bi-function in a real Hilbert space. Using certain mild conditions on the bi-function, as well as certain conditions on the iterative control parameters, proves a strong convergence theorem. The proposed algorithm uses a monotonic step size rule depending on local bi-function information. The main results are also used to solve variational inequalities and fixed-point problems. The numerical behavior of the proposed algorithm on different test problems is provided compared to other existing algorithms.

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Keywords

• Equilibrium problem
• Lipschitz-type continuity
• strong convergence
• fixed point problem
• variational inequality problem

MSC

•  47J25
•  47H09
•  47H06
•  47J05

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