A Note on: Multi-Step Approximation Schemes for the Fixed Points of Finite Family of Asymptotically Pseudocontractive Mappings

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Adesanmi Alao Mogbademu

Abstract

In this paper, using an analytical technique we obtain a strong convergence for a modified three-step iterative scheme due to Suantai [6] for asymptotically pseudocontractive mappings in real Banach spaces. Our result is an improvement and a correction of Rafiq's [4] results.

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References

  1. S. S. Chang, Some results for asymptotically pseudocontractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 129(2000), 845-853.
  2. S. S. Chang, Y. J. Cho, J. K. Kim, Some results for uniformly L-Lipschitzian mappings in Banach spaces, Applied Mathematics Letters, 22(2009), 121-125.
  3. E.U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space, J. Math. Anal. Appl., 321(2006), 722-728.
  4. A. Rafiq, Multi-step approximation schemes for the fixed points of finite family of asymptotically pseudocontractive mappings, General Mathematics, vol.19 nos. 4(2011), 41C49.
  5. J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158(1999), 407-413.
  6. S. Suantai, Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings, J. Math. Anal. Appl., 311(2005), 506-517.
  7. X. Weng, Fixed point iteration for local strictly pseudocontractive mappings, Proc. Amer. Math. Soc.113(1991), 727-731.
  8. B. Xu, M. A. Noor, Fixed point iterations for asymptotically nonexpansive map- pings in Banach spaces, J. Math. Anal. Appl., 267, 2002, 444-453.