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ArticleOriginal scientific text

Title

Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property

Authors 1, 2, 1

Affiliations

  1. Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113, U.S.A.
  2. Department of Mathematics, Lublin Technical University, 20-618 Lublin, Poland

Keywords

ENG
convergence of iterates, uniform Opial property, asymptotically nonexpansive mapping

Bibliography

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  5. R. E. Bruck, Asymptotic behavior of nonexpansive mappings, in: Contemp. Math. 18, Amer. Math. Soc., 1983, 1-47.
  6. J. M. Dye, T. Kuczumow, P.-K. Lin and S. Reich, Random products of nonexpansive mappings in spaces with the Opial property, ibid. 144, 1993, to appear.
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  8. K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174.
  9. K. Goebel and T. Kuczumow, Irregular convex sets with the fixed point property for nonexpansive mappings, Colloq. Math. 40 (1978), 259-264.
  10. J. Górnicki, Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces, Comment. Math. Univ. Carolinae 30 (1989), 249-252.
  11. J. Górnicki, Nonlinear ergodic theorems for asymptotically nonexpansive mappings in Banach spaces satisfying Opial's condition, J. Math. Anal. Appl. 161 (1991), 440-446.
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  15. T. Kuczumow, Weak convergence theorems for nonexpansive mappings and semigroups in Banach spaces with Opial's property, Proc. Amer. Math. Soc. 93 (1985), 430-432.
  16. T. Kuczumow and S. Reich, Opial's property and James' quasi-reflexive spaces, preprint.
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  19. H. Oka, Nonlinear ergodic theorems for commutative semigroups of asymptotically nonexpansive mappings, Nonlinear Anal. 18 (1992), 619-635.
  20. Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
  21. S. Prus, Banach spaces with the uniform Opial property, Nonlinear Anal. 18 (1992), 697-704.
  22. S. Reich, Nonlinear evolution equations and nonlinear ergodic theorems, ibid. 1 (1976/77), 319-330.
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  24. S. Reich, A note on the mean ergodic theorem for nonlinear semigroups, J. Math. Anal. Appl. 91 (1983), 547-551.
  25. J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, ibid. 158 (1991), 407-413.
  26. K.-K. Tan and H.-K. Xu, A nonlinear ergodic theorem for asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. 45 (1992), 25-36.
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  28. H.-K. Xu, Existence and convergence for fixed points of mappings of asymptotically nonexpansive type, Nonlinear Anal. 16 (1991), 1139-1146.
Colloquium Mathematicum
1993/65/2
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Pages:
169-179
Main language of publication
English
Received
1992-08-05
Published
1993
Exact and natural sciences