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2011 | 31 | 2 | 183-198
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Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces

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Abstrakty
EN
We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.
Twórcy
  • Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
  • Institute of Mathematics and Computer Science, Jan Dlugosz University, 42-200 Częstochowa, Poland
Bibliografia
  • [1] J. Appell and P.P. Zabrejko, Nonlinear Superposition Operators, Cambridge University Press, 1990. doi:10.1017/CBO9780511897450
  • [2] A. Azócar, J.A. Guerrero, J. Matkowski and N. Merentes, Uniformly continuous set-valued composition operators in the space of continuous functions of bounded variation in the sense of Wiener, Opuscula Math. 30 (2010), 53-60.
  • [3] V.V. Chistyakov, Lipschitzian superposition operators between spaces of functions of bounded generalized variation with weight, J. Appl. Anal. 6 (2000), 173-186. doi:10.1515/JAA.2000.173
  • [4] J.A. Guerrero, H. Leiva, J. Matkowski and N. Merentes, Uniformly continuous composition operators in the space of bounded φ-variation functions, Nonlinear Anal. 72 (2010), 3119-3123. doi:10.1016/j.na.2009.11.051
  • [5] J.J. Ludew, On Lipschitzian operators of substitution generated by set-valued functions, Opuscula Math. 27 (1) (2007), 13-24.
  • [6] J. Matkowski, Functional equations and Nemytskij operators, Funkc. Ekvacioj Ser. Int. 25 (1982), 127-132.
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  • [8] J. Matkowski, Remarks on Lipschitzian mappings and some fixed point theorems, Banach J. Math. Anal. 2 (2007), 237-244 (electronic), www.math-analysis.org.
  • [9] J. Matkowski, Uniformly continuous superposition operators in the spaces of differentiable functions and absolutely continuous functions, Internat. Ser. Numer. Math. 157 (2008), 155-155.
  • [10] J. Matkowski, Uniformly continuous superposition operators in the space of Hölder functions, J. Math. Anal. Appl. 359 (2009), 56-61. doi:10.1016/j.jmaa.2009.05.020
  • [11] J. Matkowski, Uniformly continuous superposition operators in the spaces of bounded variation functions, Math. Nachr. 283 (7) (2010), 1060-1064.
  • [12] J. Matkowski, Uniformly bounded composition operators between general Lipschitz function normed spaces, (accepted), Top. Math. Nonl. Anal.
  • [13] J. Matkowski and J. Miś, On a charakterization of Lipschitzian operators of substitution in the space BV[a,b], Math. Nachr. 117 (1984), 155-159. doi:10.1002/mana.3211170111
  • [14] K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Naukowe Politechniki Łódzkiej, Mat. 559, Rozprawy Naukowe 114, 1989.
  • [15] A. Smajdor and W. Smajdor, Jensen equation and Nemytskii operator for set-valued functions, Rad. Math. 5 (1989), 311-320.
  • [16] W. Smajdor, Note on Jensen and Pexider functional equations, Demonstratio Math. 32 (1999), 363-376.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1134
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