ISSN : 1226-0657
In this paper, we consider, under a hybrid iterative scheme with errors, a weak convergence theorem to a common element of the set of a finite family of asymptotically k-strictly pseudo-contractive mappings and a solution set of an equilibrium problem for a given bifunction, which is the approximation version of the corresponding results of Kumam et al.
H.H. Bauschke & J.M. Borwein. (1996). On projection algorithms for solving convex feasibility problems. SIAM Rev., 38, 367-426. 10.1137/S0036144593251710.
P. Kumam, N. Petrot & R. Wangkeeree. (2010). A hybrid iterative scheme for equilibrium problems and fixed point problems of asymptotically k-strict pseudo-contractions. J. Comp. Appl. Math., 233, 2013-2026. 10.1016/j.cam.2009.09.036.
E. Blum & W. Oettli. (1994). From optimization and variational inequalities to equilibrium problems. Math. Student, 63, 123-145.
P.L. Combettes & S.A. Hirstoaga. (2005). Equilibrium programming in Hilbert spaces. J. Nonlinear Convex Anal., 6, 117-136.
X. Qin, Y.J. Cho, S.M. Kang & M. Shang. (2009). A hybrid iterative scheme for asymptotically k-strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 70, 1902-1911. 10.1016/j.na.2008.02.090.
L.S. Liu. (1995). Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces. J. Math. Anal. Appl., 194, 114-115. 10.1006/jmaa.1995.1289.
G. Marino & H.K. Xu. (2007). Weak and strong convergence theorems for strict pseudo-contractions in Hilbert space. J. Math. Anal. Appl., 329, 336-346. 10.1016/j.jmaa.2006.06.055.
M.O. Osilike & D.I. Igbokwe. (2000). Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations. Comput. Math. Appl., 40, 559-567. 10.1016/S0898-1221(00)00179-6.
K.K. Tan & H.K. Xu. (1993). Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process. J. Math. Anal. Appl., 178(2), 301-308. 10.1006/jmaa.1993.1309.