Optimization Properties of Generalized Chebyshev–Poisson Integrals

Chebyshev polynomials of the first kind are applied to construct the generalized Chebyshev–Poisson integral. The optimization problem for the generalized Chebyshev–Poisson operator as a functional of a function defined on an interval is solved, and its approximate properties on Holder classes H¹ are analyzed. An exact equality is obtained for the deviation of Hölder class functions from the generalized Chebyshev–Poisson integral.