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Fixed point theorems for a semigroup of total asymptotically nonexpansive mappings in uniformly convex Banach spaces

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Języki publikacji
EN
Abstrakty
EN
In this paper, we provide existence and convergence theorems of common fixed points for left (or right) reversible semitopological semigroups of total asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results announced by other authors.
Rocznik
Strony
183--197
Opis fizyczny
Bibliogr. 36 poz.
Twórcy
autor
  • Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200, Thailand
  • Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200, Thailand
Bibliografia
  • [1] W. Takahashi, Nonlinear Functional Analysis: Fixed Point Theory and its Applications, Yokohama Publishers, Yokohama, Japan, 2000.
  • [2] R.D. Holmes, A.T. Lau, Nonexpansive actions of topological semigroups and fixed points, J. London Math. Soc. 5 (1972), 330–336.
  • [3] C. Byrne, A unified treatment of some iterative algorithms in signal processing and image construction, Inverse Probl. 20 (2004), 103-120.
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  • [5] S. Kitahara, W. Takahashi, Image recovery by convex combinations of sunny nonexpansive retractions, Topol. Methods Nonlinear Anal. 2 (1993), 333–342.
  • [6] W. Takahashi, Fixed point theorem for amenable semigroups of non-expansive mappings, Kodai Math. Sem. Rep. 21 (1969), 383–386.
  • [7] R. De Marr, Common fixed points for commuting contraction mappings, Pacific J. Math. 13 (1963), 1139–1141.
  • [8] T. Mitchell, Fixed points of reversible semigroups of nonexpansive mappings, Kodai Math. Sem. Rep. 22 (1970), 322–323.
  • [9] A.T. Lau, Invariant means on almost periodic functions and fixed point properties, Rocky Mountain J. Math. 3 (1973), 69–76.
  • [10] W. Takahashi, A nonlinear ergodic theorem for an amenable semigroup of nonexpansive mappings in a Hilbert space, Proc. Amer. Math. Soc. 81 (1981), 253–256.
  • [11] A.T. Lau, W. Takahashi, Weak convergence and nonlinear ergodic theorems for reversible semigroups of nonexpansive mappings, Pacific J. Math. 126 (1987), 177–194.
  • [12] A.T. Lau, W. Takahashi, Invariant means and semigroups of nonexpansive mappings on uniformly convex Banach spaces, J. Math. Anal. Appl. 153 (1990), 497–505.
  • [13] A.T. Lau, W. Takahashi, Invariant submeans and semigroups of nonexpansive mappings on Banach spaces with normal structure, J. Funct. Anal. 142 (1996), 79–88.
  • [14] A.T. Lau, W. Takahashi, Nonlinear submeans on semigroups, Topol. Methods Nonlinear Anal. 22 (2003), 345–353.
  • [15] A.T. Lau, H. Miyake, W. Takahashi, Approximation of fixed points for amenable semigroups of nonexpansive mappings in Banach spaces, Nonlinear Anal. 67 (2007), 1211–1225.
  • [16] A.T. Lau, Y. Zhang, Fixed point properties of semigroups of non-expansive mappings, J. Funct. Anal. 254 (2008), 2534–2554.
  • [17] B.A. Kakavandi, M. Amini, Non-linear ergodic theorem in complete non-positive curvature metric spaces, Bull. Iran. Math. Soc. 37 (2011), 11–20.
  • [18] W. Anakkanmatee, S. Dhompongsa, Rodé’s theorem on common fixed points of semigroup of nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. (2011), Article ID 34.
  • [19] G. Rodé, An ergodic theorem for semigroups of nonexpansive mappings in a Hilbert space, J. Math. Anal. Appl. 85 (1982), 172–178.
  • [20] W. Takahashi, P.J. Zhang, Asymptotic behavior of almost-orbits of semigroups of Lipschitzian mappings in Banach spaces, Kodai Math. J. 11 (1988), 129–140.
  • [21] W. Takahashi, P.J. Zhang, Asymptotic behavior of almost-orbits of semigroups of Lipschitzian mappings, J. Math. Anal. Appl. 142 (1989), 242–249.
  • [22] H.S. Kim, T.H. Kim, Asymptotic behavior of semigroups of asymptotically nonexpansive type on Banach spaces, J. Korean Math. Soc. 24 (1987), 169–178.
  • [23] H. Ishihara, W. Takahashi, A nonlinear ergodic theorem for a reversible semigroup of Lipschitzian mappings in a Hilbert space, Proc. Amer. Math. Soc. 104 (1988), 431–436.
  • [24] H.S. Kim, T.H. Kim, Weak convergence of semigroups of asymptotically nonexpansive type on a Banach space, Comm. Korean. Math. Soc. 2 (1987), 63–69.
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  • [26] A.T. Lau, Semigroup of nonexpansive mappings on a Hilbert space, J. Math. Anal. Appl. 105 (1985), 514–522.
  • [27] A.T. Lau, N. Shioji, W. Takahashi, Existence of nonexpansive retractions for amenable semigroups of nonexpansive mappings and nonlinear ergodic theorems in Banach spaces, J. Funct. Anal. 191 (1999), 62–75.
  • [28] A.T. Lau, Invariant means and fixed point properties of semigroup of nonexpansive mappings, Taiwanese J. Math. 12 (2008), 1525–1542.
  • [29] A.T. Lau, W. Takahashi, Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces, Nonlinear Anal. 70 (2009), 3837–3841.
  • [30] W. Takahashi, A nonlinear ergodic theorem for a reversible semigroup of nonexpansive mappings in a Hilbert space, Proc. Amer. Math. Soc. 97 (1986), 55–58.
  • [31] R.P. Agarwal, D. O’Regan, D.R. Sahu, Fixed Point Theory for Lipschitzian-type Mappings with Applications, Topological Fixed Point Theory and its Applications, Springer, New York, 2009.
  • [32] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 595–597.
  • [33] K. Geobel, W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.
  • [34] K. Geobel, S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, Marcel Dekker, Inc., New York, 1984.
  • [35] E. Zeidler, Nonlinear Functional and its Applications I, Springer-Verlag, New York, Heidelberg, Tokyo, 1986.
  • [36] H.K. Xu, Another control condition in an iterative method for nonexpansive mappings, Bull. Austral. Math. Soc. 65 (2002), 109–113.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-4794da5b-3a76-4982-b2e0-614dad11c242
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