Abstract. The authors establish the condition for the existence of the Chebyshev approximation by the sum of a polynomial and logarithmic expression with the smallest absolute error and Hermitian interpolation at the boundary points of an interval. The method is proposed for determining the parameters of such Chebyshev approximation.

Keywords: Chebyshev approximation, Hermitian interpolation, Remez method, alternance points.

¹ Center of Mathematical Modeling, Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

 Petro.Malachivskyy@gmail.com

² National University “Lvivska Politekhnika”, Lviv, Ukraine

 pizyur@yahoo.com

³ National University “Lvivska Politekhnika”, Lviv, Ukraine

 vasyl.a.andrunyk@lpnu.uа