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A special case of generalized Hölder functions

Lupa M.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

81--89

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.