Weak and strong convergence theorems for an asymptotically k-strict pseudo-contraction and a mixed equilibrium problem
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We introduce two iterative algorithms for finding a common element of the set of fixed points of an asymptotically k-strict pseudo-contraction and the set of solutions of a mixed equilibrium problem in a Hilbert space. We obtain some weak and strong convergence theorems by using the proposed iterative algorithms. Our results extend and improve the corresponding results of Tada and Takahashi [16] and Kim and Xu [8,9].
Abstract
We introduce two iterative algorithms for finding a common element of the set of fixed points of an asymptotically k-strict pseudo-contraction and the set of solutions of a mixed equilibrium problem in a Hilbert space. We obtain some weak and strong convergence theorems by using the proposed iterative algorithms. Our results extend and improve the corresponding results of Tada and Takahashi [16] and Kim and Xu [8,9].
참고문헌 (22)
- E. Blum, "From optimization and variational inequalities to equilibrium problems", Math. Student, 63(1), pp.123~145 (1994)
- O. Chadli, "Descent methods for equilibrium problems in a Banach space", Comput. Math. Appl., 48(3), pp.609~616 (2004)
- O. Chadli, "Regularized equilibrium problems with application to noncoercive hemivariational inequalities", J. Optim. Theory Appl., 121(3), pp.571~596 (2004)
- O. Chadli, "Equilibrium problems with applications to eigenvalue problems", J. Optim. Theory Appl., 117(2), pp.245~266 (2003)
- P. L. Combettes, "Equilibrium programming in Hilbert spaces", J. Nonlinear Convex Anal., 6(1), pp.117~136 (2005)
- X. P. Ding, "Predictor-corrector algorithms for solving generalized mixed implicit quasi-equilibrium problems", Appl. Math. Mech., 27(9), pp.1157~1164 (2006)
- S. D. Fl°am, "Equilibrium programming using proximal-like algorithms", Math. Programming, 78(1), pp.29~41 (1997), Ser. A
- T. H. Kim, "Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups", Nonlinear Anal., 64(5), pp.1140~1152 (2006)
- T. H. Kim, "Convergence of the modified Mann’s iteration method for asymptotically strict pseudo-contractions, Nonlinear Analysis", Theory, Methods & Applications, 68(9), pp.2828~2836 (2008)
- I. V. Konnov, "Combined relaxation method for mixed equilibrium problems", J. Optim. Theory Appl., 126(2), pp.309~322 (2005)
- C. Matinez-Yanes, "Strong convergence of the CQ method for fixed point iteration processes", Nonlinear Anal., 64(11), pp.2400~2411 (2006)
- M. A. Noor, "Fundamentals of equilibrium problems", Math. Inequal. Appl., 9(3), pp.529~566 (2006)
- Z. Opial, "Weak convergence of the sequence of successive approximations for nonexpansive mappings", Bull. Amer. Math. Soc., 73, pp.591~597 (1967)
- S. Plubtieng, "A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces", J. Math. Anal. Appl., 336(1), pp.455~469 (2007)
- A. Tada, "Strong convergence theorem for an equilibrium problem and a nonexpansive mapping", Nonlinear analysis and convex analysis, pp.609~617 (2007), Yokohama Publ.
- A. Tada, "Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem", J. Optim. Theory Appl, 133(3), pp.359~370 (2007)
- S. Takahashi, "Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces", J. Math. Anal. Appl., 331(1), pp.506~515 (2007)
- Y. Yao, "Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings", Fixed Point Theory Appl., pp.12~ (2007)
- Y. Yao, "A new hybrid iterative algorithm for fixed point problems, variational inequality problems and mixed equilibrium problems", Fixed Point Theory and Applications 2008, 15~ (2008)
- Y. Yao, "On iterative methods for equilibrium problems", Nonlinear Anal., 70(1), pp.497~509 (2009)
- L. C. Zeng, "A hybrid iterative scheme for mixed equilibrium problems and fixed point problems", J. Comput. Appl. Math., 214(1), pp.186~201 (2008)
- L. C. Zeng, "Generalized KKM theorem with applications to generalized minimax inequalities and generalized equilibrium problems", Taiwanese J. Math., 10(6), pp.1497~1514 (2006)
