Approximation algorithm for fixed points of nonlinear operators and solutions of mixed equilibrium problems and variational inclusion problems with applications
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Authors
Uamporn Witthayarat
- Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, KMUTT, Bangkok 10140, Thailand.
Yeol Je Cho
- Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea.
Poom Kumam
- Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, KMUTT, Bangkok 10140, Thailand.
Abstract
The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set
of fixed point of nonexpansive mappings, set of a mixed equilibrium problem and the set of variational
inclusions in a real Hilbert space. We prove that the sequence \(x_n\) which is generated by the proposed
iterative algorithm converges strongly to a common element of four sets above. Furthermore, we give an
application to optimization and some numerical examples which support our main theorem in the last part.
Our result extended and improve the existing result of Yao et al. [19] and references therein.
Share and Cite
ISRP Style
Uamporn Witthayarat, Yeol Je Cho, Poom Kumam, Approximation algorithm for fixed points of nonlinear operators and solutions of mixed equilibrium problems and variational inclusion problems with applications, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 6, 475--494
AMA Style
Witthayarat Uamporn, Cho Yeol Je, Kumam Poom, Approximation algorithm for fixed points of nonlinear operators and solutions of mixed equilibrium problems and variational inclusion problems with applications. J. Nonlinear Sci. Appl. (2012); 5(6):475--494
Chicago/Turabian Style
Witthayarat, Uamporn, Cho, Yeol Je, Kumam, Poom. "Approximation algorithm for fixed points of nonlinear operators and solutions of mixed equilibrium problems and variational inclusion problems with applications." Journal of Nonlinear Sciences and Applications, 5, no. 6 (2012): 475--494
Keywords
- Common fixed point
- Equilibrium problem
- Iterative algorithm
- Nonexpansive mapping
- Variational inequality.
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