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Article

Approximations of an Equilibrium Problem without Prior Knowledge of Lipschitz Constants in Hilbert Spaces with Applications

by
Chainarong Khanpanuk
1,
Nuttapol Pakkaranang
2,
Nopparat Wairojjana
3,* and
Nattawut Pholasa
4,*
1
Department of Mathematics, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
2
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
3
Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage (VRU), 1 Moo 20 Phaholyothin Road, Klong Neung, Klong Luang, Pathumthani 13180, Thailand
4
School of Science, University of Phayao, Phayao 56000, Thailand
*
Authors to whom correspondence should be addressed.
Axioms 2021, 10(2), 76; https://doi.org/10.3390/axioms10020076
Submission received: 21 March 2021 / Revised: 20 April 2021 / Accepted: 23 April 2021 / Published: 27 April 2021
(This article belongs to the Special Issue Numerical Analysis and Computational Mathematics)
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Abstract

The objective of this paper is to introduce an iterative method with the addition of an inertial term to solve equilibrium problems in a real Hilbert space. The proposed iterative scheme is based on the Mann-type iterative scheme and the extragradient method. By imposing certain mild conditions on a bifunction, the corresponding theorem of strong convergence in real Hilbert space is well-established. The proposed method has the advantage of requiring no knowledge of Lipschitz-type constants. The applications of our results to solve particular classes of equilibrium problems is presented. Numerical results are established to validate the proposed method’s efficiency and to compare it to other methods in the literature.
Keywords: equilibrium problem; pseudomonotone bifunction; Lipschitz-type conditions; strong convergence theorems; variational inequality problems; fixed-point problem equilibrium problem; pseudomonotone bifunction; Lipschitz-type conditions; strong convergence theorems; variational inequality problems; fixed-point problem

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MDPI and ACS Style

Khanpanuk, C.; Pakkaranang, N.; Wairojjana, N.; Pholasa, N. Approximations of an Equilibrium Problem without Prior Knowledge of Lipschitz Constants in Hilbert Spaces with Applications. Axioms 2021, 10, 76. https://doi.org/10.3390/axioms10020076

AMA Style

Khanpanuk C, Pakkaranang N, Wairojjana N, Pholasa N. Approximations of an Equilibrium Problem without Prior Knowledge of Lipschitz Constants in Hilbert Spaces with Applications. Axioms. 2021; 10(2):76. https://doi.org/10.3390/axioms10020076

Chicago/Turabian Style

Khanpanuk, Chainarong, Nuttapol Pakkaranang, Nopparat Wairojjana, and Nattawut Pholasa. 2021. "Approximations of an Equilibrium Problem without Prior Knowledge of Lipschitz Constants in Hilbert Spaces with Applications" Axioms 10, no. 2: 76. https://doi.org/10.3390/axioms10020076

APA Style

Khanpanuk, C., Pakkaranang, N., Wairojjana, N., & Pholasa, N. (2021). Approximations of an Equilibrium Problem without Prior Knowledge of Lipschitz Constants in Hilbert Spaces with Applications. Axioms, 10(2), 76. https://doi.org/10.3390/axioms10020076

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