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2 2007

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On the strong approximation of functions by the Bernstein polynomials

Michałowicz A.

Fasciculi Mathematici

2007

Nr 37

27-33

In this note we introduce the strong differences of function and its Bernstein polynomials and give approximation theorems for them. This note is motivated by results on the strong summability of trigonometric Fourier series given in [2] and by the paper [5].

On the almost periodic functions in the sense of Levitan

Michałowicz A., Stoiński S.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2007

Vol. 47, [Z] 2

149-159

In this note we present some theorems on the superposition of an (NVp)-almost periodic (a.p. for short) function, a μ-a.p. function and an (Nμ)-a.p. function. Moreover, we prove a theorem on the bounded primary function of an (NS^p)-a.p. function. Finally, we prove that the inverse of a V_p-a.p. function is (NV_p)-a.p.