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On convergence theorems of iterative schemes for pseudocontractive mappings

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In this paper, we establish the strong convergence for the Mann iterative scheme associated with uniformly continuous pseudocon- tractive mappings in real Banach spaces. Moreover, our technique of proofs is of independent interest.

Abstract

In this paper, we establish the strong convergence for the Mann iterative scheme associated with uniformly continuous pseudocon- tractive mappings in real Banach spaces. Moreover, our technique of proofs is of independent interest.

참고문헌 (13)

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  4. C. E. Chidume, "Approximate xed point sequences and convergence the- orems for Lipschitz pseudocontractive maps", Proc. Amer. Math. Soc, 132, pp.831~840 (2004)
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  7. W. R. Mann, "Mean value methods in iteration", Proc. Amer. Math. Soc, 4, pp.506~510 (1953)
  8. C. H. Morales, "Convergence of paths for pseudo-contractive mappings in Banach spaces", Proc. Amer. Math. Soc, 128, pp.3411~3419 (2000)
  9. A. Raq, "Some results on asymptotically pseudocontractive mappings", Fixed Point The- ory, 11(2), pp.355~360 (2010)
  10. B. E. Rhoades, "A comparison of various de nition of contractive mappings", Trans. Amer. Math. Soc, 226, pp.257~290 (1977)
  11. J. Schu, "Approximating xed points of Lipschitzian pseudocontractive mappings", Hous- ton J. Math, 19, pp.107~115 (1993)
  12. X. Weng, "Fixed point iteration for local strictly pseudocontractive mapping", Proc. Amer. Math. Soc, 113(3), pp.727~731 (1991)
  13. H. K. Xu, "Inequalities in Banach spaces with applications", Nonlinear Anal, 16(12), pp.1127~1138 (1991)

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