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

Volume 9, Issue 4, pp 1475--1496 http://dx.doi.org/10.22436/jnsa.009.04.07

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Authors

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].

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Keywords

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

MSC

•  47H10
•  47J25
•  65K10.

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