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

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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ISRP Style

Kanikar Muangchoo, Explicit Halpern-type iterative algorithm for solving equilibrium problems with applications, Journal of Mathematics and Computer Science, 25 (2022), no. 2, 115--132

AMA Style

Muangchoo Kanikar, Explicit Halpern-type iterative algorithm for solving equilibrium problems with applications. J Math Comput SCI-JM. (2022); 25(2):115--132

Chicago/Turabian Style

Muangchoo, Kanikar. "Explicit Halpern-type iterative algorithm for solving equilibrium problems with applications." Journal of Mathematics and Computer Science, 25, no. 2 (2022): 115--132


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