Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces

Wataru Takahashi1, Kei Zembayashi1
1Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan

Tài liệu tham khảo

Alber, 1996, Metric and generalized projection operators in Banach spaces: Properties and applications, 15 Blum, 1994, From optimization and variational inequalities to equilibrium problems, Math. Student, 63, 123 Cioranescu, 1990 Combettes, 2005, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal., 6, 117 Kamimura, 2002, Strong convergence of a proximal-type algorithm in a Banach space, SIAM J. Optim., 13, 938, 10.1137/S105262340139611X F. Kohsaka, W. Takahashi, Existence and approximation of fixed points of firmly nonexpansive type mappings in Banach spaces (in press) Matsushita, 2004, Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces, Fixed Point Theory Appl., 2004, 37, 10.1155/S1687182004310089 Matsushita, 2005, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory, 134, 257, 10.1016/j.jat.2005.02.007 Moudafi, 2003, Second-order differential proximal methods for equilibrium problems, J. Inequal. Pure Appl. Math., 4 Reich, 1996, A weak convergence theorem for the alternating method with Bregman distance, 313 Tada, 2007, Strong convergence theorem for an equilibrium problem and a nonexpansive mapping, 609 Tada, 2007, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem, J. Optim. Theory Appl., 133, 359, 10.1007/s10957-007-9187-z Takahashi, 2007, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 331, 506, 10.1016/j.jmaa.2006.08.036 Takahashi, 2000 Takahashi, 2000 Xu, 1991, Inequalities in Banach spaces with applications, Nonlinear Anal., 16, 1127, 10.1016/0362-546X(91)90200-K Zălinescu, 1983, On uniformly convex functions, J. Math. Anal. Appl., 95, 344, 10.1016/0022-247X(83)90112-9 Zălinescu, 2002