M.S. Saidusainov. Analysis of a theorem on the Jackson–Stechkin inequality in the Bergman space $B_2$ ... P. 217-224

We present a refinement of a theorem of V.A. Abilov, F.V. Abilova, and M.K. Kerimov on the exact constant in a Jackson type inequality between the mean-square approximation of a function of a complex variable by Fourier series in a system orthogonal in a bounded domain and the generalized modulus of continuity of order $m\geq 1$.

Keywords: generalized modulus of continuity, generalized translation operator, orthonormal system, Jackson-Stechkin inequality

Received Juny 28, 2018

Revised November 15, 2018

Accepted November 19, 2018

Mukim Saidusainovich Saidusaynov, Cand. Sci. (Phys.-Math.), University of Central Asia, Dushanbe, SPCE, 734013, Tajikistan, e-mail: smuqim@gmail.com

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