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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 11, Issue 2

Issues

Volume 13 (2015)

Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu

Francy Armao / Dorota Głazowska
  • Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-516, Zielona Góra, Poland
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/ Sergio Rivas / Jessica Rojas
Published Online: 2012-11-21 | DOI: https://doi.org/10.2478/s11533-012-0051-5

Abstract

We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.

MSC: 47H30; 26A45; 47B38

Keywords: Nemytskij (composition; superposition) operator; Uniformly bounded mapping; Uniformly continuous mapping; de la Vallée Poussin second-variation; Popoviciu k-th variation

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About the article

Published Online: 2012-11-21

Published in Print: 2013-02-01


Citation Information: Open Mathematics, Volume 11, Issue 2, Pages 357–367, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-012-0051-5.

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© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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