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Research Article

Approximating solutions of the generalized modification of the system of equilibrium problems and fixed point problem of a nonexpansive mapping

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Pages 1821-1838 | Received 11 Mar 2020, Accepted 18 May 2023, Published online: 04 Jun 2023
 

Abstract

The purpose of this research is to study the generalized modification of the system of equilibrium problems (GMSEP) and a lemma is established to show the property of this problem. Then, we prove a strong convergence theorem for finding a common element of the set of the solutions of the fixed points problem and the set of the solutions of the GMSEP under some suitable conditions, in which αn+βn+δn1, where {αn},{βn},{δn} are coefficients in the main iteration. Moreover, we prove strong convergence theorems for finding solutions to the generalized equilibrium problem, the system of equilibrium problems, the variational inequality problem, the general system of variational inequality problems, and the minimization problem. Finally, we give two numerical examples, one of which shows the rate of convergence of the main iteration while the other shows the rate of convergence of the main iteration but the sum of coefficients equals 1.

Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by King Mongkut's Institute of Technology Ladkrabang.

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