PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let C be a ρ-bounded, ρ -closed, convex subset of a modular function space Lρ. We investigate the existence of common fixed points for semigroups of nonlinear mappings Tt : C → C, i.e. a family such that T0(x) = x, Ts+t = Ts(Tt(x)), where each Tt is either ρ -contraction or ρ -nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.
Rocznik
Strony
81--98
Opis fizyczny
Bibliogr. 32 poz.
Twórcy
Bibliografia
  • [1] L.P. Belluce, and W.A. Kirk, Fixed-point theorems for families of contraction mappings, Pacific. J. Math., 18 (1966), 213 - 217.
  • [2] L.P. Belluce, and W.A. Kirk, Nonexpansive mappings and fixed-points in Banach spaces, Illinois. J. Math., 11 (1967), 474 - 479.
  • [3] H. Brezis, E. Lieb A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., 88.3 (1983), 486-490.
  • [4] F.E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 1041-1044.
  • [5] R.E. Bruck, A common fixed point theorem for a commuting family of nonexpansive mappings, Pacific. J. Math., 53 (1974), 59 - 71.
  • [6] J. Cerda, H. Hudzik, and M. Mastylo, On the geometry of some Calderon-Lozanovskii interpolation spaces, Indagationes Math., 6.1 (1995), 35 - 49.
  • [7] R.E. DeMarr, Common fixed-points for commuting contraction mappings, Pacific. J. Math., 13 (1963), 1139 - 1141.
  • [8] J.R. Dorroch, and J.W. Neuberger, Linear extensions of nonlinear semigroups, Semigroups and Operators: Theory and Applications, A.V. Balakrishnan, Ed., Birkhauser (2000), 96 - 102.
  • [9] A. Haji, and E. Hanebaly, Perturbed integral equations in modular function spaces, Electronic J. of Qualitative Theory of Diff. Equations, 20.1-7 (2003), http://www.math.uszeged. hu/ejqtde/
  • [10] N. Hussain, and M.A. Khamsi, On asymptotic pointwise contractions in metric spaces, Nonlinear Analysis, 71.10 (2009), 4423 - 4429.
  • [11] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19.4 (1967), 508 - 520.
  • [12] M.A. Khamsi, Nonlinear Semigroups in Modular function spaces, Math. Japonica, 37.2 (1992), 1-9.
  • [13] M.A. Khamsi, A convexity property in Modular function spaces, Math. Japonica, 44.2 (1996), 269-279.
  • [14] M.A. Khamsi, and W.K. Kozlowski, On asymptotic pointwise contractions in modular function spaces, Nonlinear Analysis, 73 (2010), 2957 - 2967.
  • [15] M.A. Khamsi, and W.K. Kozlowski, On asymptotic pointwise nonexpansive mappings in modular function spaces, J. Math. Anal. Appl.(2011), doi:10.1016/j.jmaa.2011.03.031.
  • [16] M.A. Khamsi, W.K. Kozlowski, and S. Reich, Fixed point theory in modular function spaces, Nonlinear Analysis, 14 (1990), 935-953.
  • [17] M.A. Khamsi, W.M. Kozlowski, and C. Shutao, Some geometrical properties and fixed point theorems in Orlicz spaces, J. Math. Anal. Appl., 155.2 (1991), 393-412.
  • [18] W. A. Kirk, and H.K. Xu, Asymptotic pointwise contractions, Nonlinear Anal., 69 (2008), 4706 - 4712.
  • [19] W.M. Kozlowski, Notes on modular function spaces I, Comment. Math., 28 (1988), 91-104.
  • [20] W.M. Kozlowski, Notes on modular function spaces II, Comment. Math., 28 (1988), 105-120.
  • [21] W.M. Kozlowski, Modular Function Spaces, Series of Monographs and Textbooks in Pure and Applied Mathematics, Vol.122, Dekker, New York/Basel, 1988.
  • [22] W.M. Kozlowski, Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 377 (2011) 4352
  • [23] W.M. Kozlowski, Common fixed points for semigroups of pointwise Lipschitzian mappings in Banach spaces, to appear
  • [24] T.C. Lim, A fixed point theorem for families of nonexpansive mappings, Pacific. J. Math., 53 (1974), 487 - 493.
  • [25] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, Vol.1034, Springer-Verlag, Berlin/Heidelberg/New York/Tokyo, 1983.
  • [26] I. Miyaderau, Nonlinear ergodic theorems for semigroups of non-Lipschitzian mappings in Banach spaces, Nonlinear Anal., 50 (2002), 27 - 39.
  • [27] S. Oharu, Note on the representation of semi-groups of non-linear operators, Proc. Japan. Acad., 42 (1967), 1149 - 1154.
  • [28] J. Peng, and S-K. Chung, Laplace transforms and generators of semigroups of operators, Proc. Amer. Math. Soc., 126.8 (1998), 2407 - 2416.
  • [29] J. Peng, and Z. Xu, A novel approach to nonlinear semigroups of Lipschitz operators, Trans. Amer. Math. Soc., 367.1 (2004), 409 - 424.
  • [30] S. Reich, A note on the mean ergodic theorem for nonlinear semigroups, J. Math. Anal. Appl., 91 (1983), 547 - 551.
  • [31] A. Ait Taleb, and E.Hanebaly, A fixed point theorem and its application to integral equations in modular function spaces, Proc. Amer. Math. Soc., 128.2 (1999), 419 - 427.
  • [32] K-K.Tan, and H-K. Xu, An ergodic theorem for nonlinear semigroups of Lipschitzian mappings in Banach spaces, Nonlinear Anal., 19.9 (1992), 805 - 813.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0012-0016
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.