##### Title: Convergence Theorems of an Implicit Iterates with Errors for Total Asymptotically Pseudo-Contractive Mappings

##### Pages: 54-61

##### Cite as:

G.S. Saluja, Convergence Theorems of an Implicit Iterates with Errors for Total Asymptotically Pseudo-Contractive Mappings, Int. J. Anal. Appl., 2 (1) (2013), 54-61.#### 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.

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#### 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.