ON THE OPTIMIZATION PROPERTIES OF GENERALIZED CHEBYSHEV–POISSON INTEGRALS

Abstract

Chebyshev polynomials of the first kind are used to construct the generalized Chebyshev–Poisson integral. The optimization problem for the generalized Chebyshev–Poisson operator as a functional of a function defined on a segment is solved, and its approximate properties on Hölder classes H 1 are analyzed. An exact equality is obtained for the deviation of Hölder class functions from the generalized Chebyshev–Poisson integral. Keywords: Chebyshev polynomials, generalized Chebyshev–Poisson integral, class of Hölder functions, optimization problem.