Scientific Journal of Samarkand University


The paper is devoted to some generalizations and improvements of results obtained in the paper [1] of the best joint polynomial approximations in uniform and integral metrics on a given bounded closed convex domain of the functions of many real variables (FMRV) from the seminormalized Sobolev space with last derivative of integrable on nonempty intersections of each straight line with this domain.

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1. A. Khatamov. On the best Polynomial Approximations of Functions of Many Real Variables From the Sobolev Space with Derivatives of bounded Variation, TWMS Jourmal of Pure and Applied Math. V.2, N.2, pp. 236- 246, 2011. 2. A. Khatamov. Polynomial and Rational Approximations of Functions in Many Variables with Convex Derivatives in � � (� < � ≤ ∞) Metrics, Rossiyskaya Akad. Nauk, Seriya Matem. [Russian Academy of Sciences, Math. Series], 58,No.1, 167- 181, 1994. 3. V.N.Konovalov. Approximation of functions of several variables by polynomials preserving the difference- differential properties, Ukrain Math. Zh. [UkrainianMath. J.], 36 (2), pp. 154- 159, 1984.

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