Convergent problem of iterative sequences for nonlinear mappings with error members in banach spaces
Tóm tắt
In this paper, the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated. Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively. The results thus extend and improve some recent corresponding results.
Tài liệu tham khảo
Goebel, K., Kirk, W. A., A Fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 1972,35(1):171–174.
Schu, J., Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 1991, 158:407–413.
Chidume, C. E., An iterative process for nonlinear Lipschitzian strongly accretive mappings in L p spaces, J. Math. Anal. Appl., 1990,151:453–461.
Chidum, C. E., Approximation of fixed points of strongly pseudo-contractive mappings, Proc. Amer. Math. Soc., 1994,120:545–551.
Xu, H. K., Existence and convergence for fixed points of mapping of asymptotically nonexpansive type, Nonlinear Anal., 1991,16(12):1139–1146.
Liu, Q., Convergence theorems of the sequence of iterates for asymptotically demi-contractive and hemi-contractive mappings, Nonlinear Anal., 1996,26(11):1835–1842.
Chang, S. S., Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 2001,129:845–853.
Xu, Y., Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl., 1998,224:91–101.
Chang, S. S., Iterative approximation problem of fixed points for asymptotically nonexpansive mappings in Banach spaces, Acta. Math. Appl. Sinica, 2001,24(2):236–241. (in Chinese)
Liu, L. S., Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl., 1995,194:114–125.
Xu, Z. B., Roach, G. F., A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations, J. Math. Anal. Appl., 1992,167:340–354.