Convergence Theorems of an Implicit Iterates with Errors for Total Asymptotically Pseudo-Contractive Mappings
Main Article Content
Abstract
The goal of this paper is to establish weak and strong convergence theorems of an implicit iteration process with errors to converge to common fixed points for a finite family of uniformly $L$-Lipschitzian total asymptotically pseudo-contractive mappings in the framework of Banach spaces. Our results extend the corresponding result of [2.5.8.10] and many others.
Article Details
References
- G.L. Acedo and H.K. Xu, Iterative methods for strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 67(2007), 2258-2271.
- S.S. Chang, On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 313 (2006), 273-283.
- C.E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal., TMA, 62 (2005), no. 6, 1149-1156.
- G. Marino and H.K. Xu, Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces, J. Math. Anal. Appl. 329(2007), 336-346.
- Q. Miao, R. Chen and H. Zhou, Convergence of an implicit iteration process for a finite family of total asymptotically pseudocontractive maps, Int. J. Math. Anal. Vol.2, no.9 (2008), 433-436.
- Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73(1967), 591-597.
- M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294(1)(2004), 73-81.
- M.O. Osilike and B.G. Akuchu, Common fixed points of a finite family of asymptotically pseudocontractive maps, Fixed Point Theory and Applications 2 (2004), 81-88.
- M.O. Osilike, S.C. Aniagbosor and B.G. Akuchu, Fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces, PanAm. Math. J. 12 (2002), 77-78.
- Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003), 351-358.
- H.K. Xu and R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22(2001), 767-773.
- Y.Y. Zhou and S.S. Chang, Convergence of implicit iteration processes for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 23(2002), 911-921.