Schramm spaces and composition operators

• Autorzy: Wróbel Małgorzata

Identyfikatory

DOI

10.17512/jamcm.2023.2.08

• Języki publikacji: EN

Abstrakty

EN

We give some properties of Schramm functions; among others, we prove that the family of all continuous piecewise linear functions defined on a real interval I is contained in the space ΦBV (I) of functions of bounded variation in the sense of Schramm. Moreover, we show that the generating function of the corresponding Nemytskij composition operator acting between Banach spaces CΦBV (I) of continuous functions of bounded Schramm variation has to be continuous and additionally we show that a space CΦBV (I) has the Matkowski property.

Słowa kluczowe

EN

Schramm function; continuous function; Nemytskij composition operator; Schramm type variation; uniformly continuous operator; Lipschitz operator

PL

funkcja Schramma; funkcja ciągła; operator kompozycji Niemyckiego; operator jednostajnie ciągły; operator Lipschitza

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2023
• Tom: Vol. 22, nr 2
• Strony: 87--98
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Wróbel Małgorzata

• Department of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

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• [3] Grützner, S., & Muntean, A. (2021). Identifying processes governing damage evolution in quasistatic elasticity, Part 1- Analysis. Advances in Mathematical Sciences and Applications, 30(2), 305-334.
• [4] Krämer, R, & Mathé, P. (2008). Modulus of continuity of Nemytskii operators with application to the problem of option pricing. Journal of Inverse and Ill-posed Problems, 16(5), 435-461.
• [5] Appell, J., Banaś, J., & Merentes, N. (2014). Bounded Variation and Around. Berlin, Boston: De Gruyter.
• [6] Ereu, T., Merentes, N., Sanchez, J.L., & Wróbel, M. (2012). Uniformly continuous composition operators in the space of bounded Φ-variation functions in the Schramm sense. Opuscula Mathematica, 32, 239-249.
• [7] Guerrero, J.A, Leiva, H., Matkowski, J., & Merentes, N. (2010). Uniformly continuous composition operators in the space of bounded ϕ-variation functions. Nonlinear Analysis, 72, 3119-3123.
• [8] Schramm, M. (1985). Funtions of φ -bounded variation and Riemann Stieltjes integration. Transactions of the American Mathemetical Society, 267, 49-63.
• [9] Wróbel, M. (2021). The form of locally defined operators in Waterman spaces. Mathematica Slovaca, 71(6), 1529-1544.
• [10] Matkowski, J. (1982). Functional equation and Nemytskij operators. Funkcial Ekv., 25, 127-132.
• [11] Matkowski, J., & Miś, J. (1984). On a characterization of Lipschitzian operators of substitution in the space BV [a,b]. Mathematische Nachrichten, 117, 155-159.
• [12] Matkowski, J. (2010). Uniformly continuous superposition operators in the spaces of bounded variation functions. Math. Nach., 283(7), 1060-1064.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).