Annals of Functional Analysis

On an iteration process for common fixed points of nonself total asymptotically nonexpansive mappings in Banach spaces.

Safeer Hussain Khan, Hukmi Kiziltunc, and Yunus Purtas

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Abstract

In this paper, we prove some weak and strong convergence results for a generalized three-step-three-mappings iteration scheme using a more satisfactory definition of nonself mappings. Our results approximate common fixed points of three nonself total asymptotically nonexpansive mappings in a uniformly convex Banach space.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 1 (2015), 235-248.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1419001463

Digital Object Identifier
doi:10.15352/afa/06-1-18

Mathematical Reviews number (MathSciNet)
MR3297800

Zentralblatt MATH identifier
1312.47082

Subjects
Primary: 47J05
Secondary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
Nonself total asymptotically strong and weak convergence common fixed point uniformly convex Banach spaces

Citation

Khan, Safeer Hussain; Kiziltunc, Hukmi; Purtas, Yunus. On an iteration process for common fixed points of nonself total asymptotically nonexpansive mappings in Banach spaces. Ann. Funct. Anal. 6 (2015), no. 1, 235--248. doi:10.15352/afa/06-1-18. https://projecteuclid.org/euclid.afa/1419001463


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References

  • Y.I. Alber, C.E. Chidume and H. Zegeye, Approximating fixed points of total asymptotically nonexpansive mappings, Hind. Publis. Corp. Fixed Point Theory Appl., Article ID 10673 (2006), 1-20.
  • C.E. Chidume and E.U. Ofoedu, Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings, J. Math. Anal. Appl. 333 (2007), 128-141.
  • C.E. Chidume, E.U, Ofoedu and H. Zegeye, Strong and weak convergence theorems for asymptotically nonexpansive mappings, J. Math. Anal. Appl. 280 (2003), 364-374.
  • K. Goebel and W.A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174.
  • G. Hu and L. Yang, Strong convergence of the modified three step iterative process in Banach spaces, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 15 (2008), 555-571.
  • S.H. Khan and N. Hussain, Convergence theorems for nonself asymptotically nonexpansive mappings, Comp. Math. App. 55 (2008), 2544-2553.
  • E. Lami Dozo, Multivalued nonexpansive mappings and Opial's condition, Proc. Amer. Math. Soc. 38 (1973), 286-292.
  • F. Mukhamedov and M. Saburov, Strong Convergence of an Explicit Iteration Process for a Totally Asymptotically $I$ -Nonexpansive Mapping in Banach Spaces, Appl. Math. Lett. (2010), 1473-1478.
  • R.A. Rashwan and S.M. Altwqi, Convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings, Int. J. Pure Appl. Math. 70 (2011), 503-520.
  • K.K. Tan and H.K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308.
  • S. Thianwan, Common fixed point of new iterations for two asymptotically nonexpansive nonself mappings in a Banach space, J. Comput. Appl. Math. 224 (2009), 688-695.
  • Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
  • H.K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal. 16 (1991), 1127-1138.