On a certain property of generalized Hölder functions

• Autorzy: Lupa M.

Identyfikatory

DOI

10.17512/jamcm.2015.4.12

• Języki publikacji: EN

Abstrakty

EN

In this paper some properties of functions belonging to the space Wy[a,b] of generalized Hölder functions 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 fundamental lemma that the recursive model-defined functions ℎk: I × Rk+1 → R, k = 0,1, … , r are a special form and belong to the space Wy[a,b].

Słowa kluczowe

EN

Lipschitz condition; generalized Hölder condition; y-Hölder condition

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2015
• Tom: Vol. 14, nr 4
• Strony: 127--132
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Lupa M.

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

Bibliografia

• [1] Lupa M., A special case of generalized Hölder functions, Journal of Applied Mathematics and Computational Mechanics 2014, 13, 4, 81-89.
• [2] Kuczma M., Functional Equations in a Single Variable, PWN, Warszawa 1968.
• [3] Kuczma M., Choczewski B., Ger R., Iterative Functional Equations, Cambridge University Press, Cambridge-New York-Port Chester-Melbourne-Sydney 1990.
• [4] Lupa M., On solutions of a functional equation in a special class of functions, Demonstratio Mathematica 1993, XXVI, 1, 137-147.
• [5] Lupa M., Wγ - solutions of linear Iterative Functional Equations, Demonstratio Mathematica 1994, XXVII, 2, 417-425.