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2021•Rocky Mountain Journal of MathematicsOpen access

Jackson-type inequalities and widths of functional classes in the Musielak–Orlicz type spaces

Fahreddin G. Abdullayev, Stanislav O. Chaichenko, Meerim Imashkyzy, Andrii Shidlich

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Abstract

In the Musielak–Orlicz-type spaces 𝒮M, exact Jackson-type inequalities are obtained in terms of best approximations of functions and the averaged values of their generalized moduli of smoothness. The values of Kolmogorov, Bernstein, linear, and projective widths in 𝒮M are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.

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In the Musielak–Orlicz-type spaces 𝒮M, exact Jackson-type inequalities are obtained in terms of best approximations of functions and the averaged values of their generalized moduli of smoothness. The values of Kolmogorov, Bernstein, linear, and projective widths in 𝒮M are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.

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Available abstract

In the Musielak–Orlicz-type spaces 𝒮M, exact Jackson-type inequalities are obtained in terms of best approximations of functions and the averaged values of their generalized moduli of smoothness. The values of Kolmogorov, Bernstein, linear, and projective widths in 𝒮M are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.

Key concepts: Mathematics, Smoothness, Type (biology), Moduli, Pure mathematics, Mathematical analysis, Physics, Ecology

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