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Exact Inequalities between the Best Polynomial Approximations and Averaged Norms of Finite Differences in the B2 Space and Widths of Some Classes of Functions

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Abstract

In this paper, exact constants in Jackson–Stechkin-type inequalities for characterizing the smoothness of the functions Λm(f), m ∈ ℕ, defined by averaging the norms of mth-order finite differences of the function f over the argument z = ρeit analytic in the unit disk U := {z : |z| < 1} belonging to the Bergman space B2 are found. For the classes of analytic functions in the disk U, defined by the characteristics of smoothness Λm(f) and Φ majorants, satisfying a number of conditions, the exact values of various n-widths are calculated.

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  1. Institute of Tourism, Entrepreneurship, and Service, 734005, Dushanbe, Republic of Tajikistan

    Kh. M. Khuromonov

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  1. Kh. M. Khuromonov
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Correspondence to Kh. M. Khuromonov.

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Translated by E. Oborin

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Khuromonov, K.M. Exact Inequalities between the Best Polynomial Approximations and Averaged Norms of Finite Differences in the B2 Space and Widths of Some Classes of Functions. Russ Math. 66, 50–58 (2022). https://doi.org/10.3103/S1066369X22030045

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