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1993 | 65 | 2 | 169-179
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Rocznik
Tom
65
Numer
2
Strony
169-179
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-08-05
Twórcy
autor
  • Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113, U.S.A.
  • Department of Mathematics, Lublin Technical University, 20-618 Lublin, Poland
autor
  • Department of Mathematics, University of Southern California, Los Angeles, California 90089-1113, U.S.A.
Bibliografia
  • [1] J.-B. Baillon, Un théorème de type ergodique pour les contractions non linéaires dans un espace de Hilbert, C. R. Acad. Sci. Paris Sér. A 280 (1975), 1511-1514.
  • [2] J.-B. Baillon and R. E. Bruck, Ergodic theorems and the asymptotic behavior of contraction semigroups, preprint.
  • [3] H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983), 486-490.
  • [4] R. E. Bruck, On the almost-convergence of iterates of a nonexpansive mapping in Hilbert space and the structure of the weak ω-limit set, Israel J. Math. 29 (1978), 1-16.
  • [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.
  • [7] M. Edelstein and R. C. O'Brien, Nonexpansive mappings, asymptotic regularity, and successive approximations, J. London Math. Soc. (2) 1 (1978), 547-554.
  • [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.
  • [12] J. P. Gossez and E. Lami-Dozo, Some geometric properties related to the fixed point theory for nonexpansive mappings, Pacific J. Math. 40 (1972), 565-575.
  • [13] S. Ishikawa, Fixed points and iterations of nonexpansive mappings in Banach space, Proc. Amer. Math. Soc. 5 (1976), 65-71.
  • [14] W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339-346.
  • [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.
  • [17] C. Lennard, A new convexity property that implies a fixed point property for $L_1$, Studia Math. 100 (1991), 95-108.
  • [18] T. C. Lim, Asymptotic center and nonexpansive mappings in conjugate Banach spaces, Pacific J. Math. 90 (1980), 135-143.
  • [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.
  • [23] S. Reich, Almost convergence and nonlinear ergodic theorems, J. Approx. Theory 24 (1978), 269-272.
  • [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.
  • [27] D. Tingley, An asymptotically nonexpansive commutative semigroup with no fixed points, Proc. Amer. Math. Soc. 97 (1986), 107-113.
  • [28] H.-K. Xu, Existence and convergence for fixed points of mappings of asymptotically nonexpansive type, Nonlinear Anal. 16 (1991), 1139-1146.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv65i2p169bwm
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