An iterative approximation scheme for solving a split generalized equilibrium, variational inequalities and fixed point problems

ABSTRACT

In this paper, we consider a common solution of three problems in Hilbert spaces including the split generalized equilibrium problem, the variational inequality problem and fixed point problem. For finding the solution, we present a new iterative method and prove the strongly convergence theorem under mild conditions. Moreover, some numerical examples are given in the last section.

Keywords:

• Fixed point
• variational inequality
• viscosity approximation method
• non-expansive mapping
• Hilbert space
• split generalized equilibrium problem
• strong convergence

2010 Mathematics Subject Classifications:

• 46C05
• 47H09
• 47H10
• 47J25
• 90C33

Acknowledgments

All authors contributed equally and significantly in writing this paper. The authors would to thanks the referees and Professor Jesus Vigo Aguiar for reading this paper carefully, providing valuable suggestions and comments, and pointing out a major error in the original version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Poom Kumam  http://orcid.org/0000-0002-5463-4581

Additional information

Funding

This project was supported by the Theoretical and Computational Science (TaCS) Center under Computational and Applied Science for Smart Innovation Research Cluster (CLASSIC), Faculty of Science, KMUTT. The first author was funded by King Mongkut's University of Technology North Bangkok [No.KMUTNB-ART-60-057]. Moreover, Poom Kumam was supported by the Thailand Research Fund and the King Mongkut's University of Technology Thonburi under the TRF Research Scholar [Grant No.RSA5780059].