An iterative method for solving equilibrium problem fixed point problem and generalized variational inequalities problem
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In this paper, we introduce a new iterative scheme for nding a common element of the set of an equilibrium problem, the set of xed points of nonexpansive mapping and the set of solutions of the generalized variational inequality for α-inverse strongly g-monotone mapping in a Hilbert space. Under suitable conditions, strong convergence theorems for approximating a common element of the above three sets are obtained.
Abstract
In this paper, we introduce a new iterative scheme for nding a common element of the set of an equilibrium problem, the set of xed points of nonexpansive mapping and the set of solutions of the generalized variational inequality for α-inverse strongly g-monotone mapping in a Hilbert space. Under suitable conditions, strong convergence theorems for approximating a common element of the above three sets are obtained.
참고문헌 (8)
- M. Aslam Noor, "General variational inequalities", Appl. Math. Lett, (1), pp.119~121 (1988)
- G. Stampacchia, "Fromes bilineaires sur les ensembles convexes", C. R. Acad. Sci. Paris, (258), pp.4413~4416 (1964)
- L. Zhang, "Viscosity approximation methods for nonexpansive mappings and Generalized Variational Inequalities", Acta Mathematica Sinica, Chinese Series, 4(53), pp.691~698 (2010)
- Y. Su, "An iterative method of solution for equilibrium and opti-mization problems", Nonlinear Analysis, (69), pp.2709~2719 (2008)
- E. Blum, "From optimization and variational inequalities to equilibrium problems", Math. Student, (63), pp.123~145 (1994)
- P. L. Combettes, "Equilibrium programming using proximal-like algorithms", Math. Program, (78), pp.29~41 (1997)
- A. Goebel, "Topics in Metric Fixed Point Theory, Cambridge Studies in Advanced Mathematics 28" (1990), Cambridge University Press
- H. K. Xu, "An iterative approach to quadratic optimization", J. Optim. Theory Appl, (116), pp.659~678 (2003)
