The article discusses a method for constructing a spline Triac 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 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 is constructed.
Then, estimates are obtained for the best approximation, variation, and modulus of continuity of a given spline Wall Taps function.Section 3 contains evidence of the main results and final comments.