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Tytuł artykułu

Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Riesz

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show that any uniformly continuous and convex compact valued Nemytskii composition operator acting in the spaces of functions of bounded φ-variation in the sense of Riesz is generated by an affine function.
Rocznik
Strony
39--45
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
autor
autor
  • Departarnento de Ffsica y Matematica, Universidad de Los Andes, Trujillo, Venezuela, wadie@ula.ve
Bibliografia
  • [1] J. Appell and P. P. Zabrejko, Nonlinear Superposition Operators, Cambridge Univ. Press, New York, 1990.
  • [2] V. V. Chistyakov, Generalized variation of mappings with applications to composition operators and multifunctions, Positivity 5 (2001), 323-358.
  • [3] A. Acosta, W. Aziz, J. Matkowski, and N. Merentes, Uniformly continuous composition operator in the space of φ-variation functions in the sense of Riesz, Fasc. Math. 43 (2010), 5-11.
  • [4] J. Matkowski, Lipschitzian composition operators in some function spaces, Nonlinear Anal. 3 (1997), 719-726.
  • [5] J. Matkowski, Uniformly continuous superposition operators in the space of differentiable functions and absolutely continuous functions, in: Int. Ser. Numer. Math. 157, Birkhäuser, 2008, 155-166.
  • [6] J. Matkowski, Uniformly continuous superposition operators in the space of Holder functions, J. Math. Anal. Appl. 359 (2009), 56-61.
  • [7] J. Matkowski, Uniformly continuous superposition operators in the space of bounded variation functions, Math. Nachr., to appear.
  • [8] J. Matkowski and J. Miś, On a characterization of Lipschitzian operators of substitution in the space BV(a,b), Math. Nachr., 117 (1984), 155-159.
  • [9] N. Merentes, Composition of functions of bounded (φ-variation, Pure Math. Appl. Ser. B 1 (1991), 39-45.
  • [10] K. Nikodem, K-convex and K-concave set-valued functions, Politech. Lódz. Zeszyty Nauk. 559 (1989).
  • [11] H. Rädström, An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
  • [12] A. Smajdor and W. Smajdor, Jensen equation and Nemytskii operator for set-valued functions, Rad. Mat. 5 (1989), 311-320.
  • [13] G. Zawadzka, On Lipschitzian operators of substitution in the space of set-valued functions of bounded variation, ibid. 6 (1990), 279-293.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0049-0005
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