# A viscosity of Cesaro mean approximation method for split generalized equilibrium, variational inequality and fixed point problems

Volume 9, Issue 4, pp 1475--1496 Publication Date: April 20, 2016
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Jitsupa Deepho - Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok 10140, Thailand. - Department of Mathematics, Faculty of Science, University of Jaén, Campus Las Lagunillas, s/n, 23071 Jaén, Spain. Juan Martínez-Moreno - Department of Mathematics, Faculty of Science, University of Jaén, Campus Las Lagunillas, s/n, 23071 Jaén, Spain. Poom Kumam - Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok 10140, Thailand. - Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.

### Abstract

In this paper, we introduce and study an iterative viscosity approximation method by modified Cesàro mean approximation for finding a common solution of split generalized equilibrium, variational inequality and fixed point problems. Under suitable conditions, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. The results presented in this paper generalize, extend and improve the corresponding results of Shimizu and Takahashi [K. Shimoji, W. Takahashi, Taiwanese J. Math., 5 (2001), 387-404].

### Keywords

• Fixed point
• variational inequality
• viscosity approximation
• nonexpansive mapping
• Hilbert space
• split generalized equilibrium problem
• Cesàro mean approximation method.

•  47H10
•  47J25
•  65K10.

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