A special case of generalized Hölder functions

• Autorzy: Lupa M.
• Języki publikacji: EN

Abstrakty

EN

In this paper some properties of a special case of generalized Hölder functions, which belong to the space W γ [a, b], are considered. These functions are r-times differentiable and their r-th derivatives satisfy the generalized Hölder condition. The main result of the paper is a proof of the theorem that product of two functions belonging to the space W γ [a, b] also belongs to this space.

Słowa kluczowe

EN

Lipschitz condition; generalized Hölder condition; equivalency of norms

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 4
• Strony: 81--89
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Lupa M.

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

Bibliografia

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• [3] Matkowski J., Form of Lipschitz operators of substitution in Banach space of differentiable functions, Zeszyty Naukowe Politechniki Łódzkiej, Matematyka, 1982, 25, 127-132.
• [4] Matkowski J., Miś J., On a characterization of Lipschitzian operators of substitution in the space BV[a,b], Math. Nachr. 1984, 117, 155-159.
• [5] Appell J., Banaś J., Merentes N., Bounded Variation and Around, De Gruyter Studies in Nonlinear Analysis and Applications, Volume 17, Würzburg 2014.
• [6] Appell J., Zabrejko P.P., Nonlinear Superposition Operators, Cambridge University Press, Cambridge- New York-Port Chester-Melbourne-Sydney 1990.
• [7] Lupa M., Form of Lipschitzian operator of substitution in some class of functions, Zeszyty Naukowe Politechniki Łódzkiej, Matematyka, 1990, 21, 87-96.
• [8] Lupa M., On solutions of a functional equation in a special class of functions, Demonstratio Mathematica 1993, XXVI, 1, 137-147.
• [9] Lupa M., W gamma - solutions of linear Iterative Functional Equations, Demonstratio Mathematica 1994, XXVII, 2, 417-425.