On the approximation of bounded functions by trigonometric polynomials in Hausdorff metric

On the approximation of bounded functions by trigonometric polynomials in Hausdorff metric

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The article discusses a method for constructing a spline function to obtain estimates that are exact in order to approximate bounded functions by trigonometric polynomials in the Hausdorff metric.The introduction provides a brief history of approximation of continuous and bounded functions in SEABUCKTHORN BERRY LOTION the uniform metric and the Hausdorff metric.Section 1 contains the main definitions, necessary facts, and formulates the main result.An estimate for the indicated approximations is obtained from Jackson's inequality for uniform approximations.In section 2 auxiliary statements are proved.

So, for an arbitrary $2pi$-periodic bounded function, a spline function Spoon Set is constructed.Then, estimates are obtained for the best approximation, variation, and modulus of continuity of a given spline function.Section 3  contains evidence of the main results and final comments.