Paper Info
Title
The modified Noor iterations with errors for non-Lipschitzian mappings in Banach spaces
Abstract
In this paper, weak and strong convergence theorems are established for the modified Noor iterations with errors for asymptotically nonexpansive mappings in the intermediate sense in a uniformly convex Banach space. Mann-type and Ishikawa-type iterations are included by the modified Noor iterations with errors. The results obtained in this paper extend and improve the recent ones announced by Schu [J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991) 407-413; J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 43 (1991) 153-159], Xu and Noor [B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453], Cho et al. [Y.J. Cho, H.Y. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707-717], Suantai [S. Suantai, Weak and strong convergence criteria of Noor Iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 311 (2005) 506-517], Nammanee et al. [K. Nammanee, M.A. Noor, S. Suantai, Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 314 (2006) 320-334], and many others.
Year
DOI
Venue
2007
10.1016/j.amc.2006.08.081
Applied Mathematics and Computation
Keywords
Field
DocType
j. math,m.a. noor,j. schu,strong convergence theorem,non-lipschitzian mapping,opial’s condition,modified noor iteration,fixed point,s. suantai,banach space,asymptotically nonexpansive mapping,convergence criterion,asymptotically nonexpansive mapping in the intermediate sense,completely continuous,noor iterations,uniformly convex banach space,fixed point iteration
Convergence (routing),Weak convergence,Mathematical optimization,Iterative method,Mathematical analysis,Banach space,Regular polygon,Fixed point,Numerical analysis,Mathematics
Journal
Volume
Issue
ISSN
187
2
Applied Mathematics and Computation
Citations 
PageRank 
References 
2
0.68
0
Authors
2
Name
Order
Citations
PageRank
Kamonrat Nammanee121.35
Suthep Suantai24315.06