On the value of the widths of some classes of functions from L_2 | Zendy

М. Р. Лангаршоев | Zendy

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On the value of the widths of some classes of functions from L_2

Author(s) -

М. Р. Лангаршоев

Publication year - 2021

Publication title -

dal nevostochnyi matematicheskii zhurnal

Language(s) - English

Resource type - Journals

ISSN - 1608-845X

DOI - 10.47910/femj202106

Subject(s) - mathematics , modulus of continuity , differentiable function , pure mathematics , trigonometry , moduli , trigonometric functions , derivative (finance) , periodic function , type (biology) , order (exchange) , value (mathematics) , mathematical analysis , space (punctuation) , function (biology) , trigonometric polynomial , second derivative , geometry , physics , statistics , quantum mechanics , ecology , linguistics , philosophy , finance , evolutionary biology , financial economics , economics , biology

In this paper we find sharp inequalities of Jackson-Stechkin type between the best approximations of periodic differentiable functions by trigonometric polynomials and generalized moduli of continuity of m-th order in the space L_2. The exact values of various n-widths of classes of functions from L_2 defined by the generalized modus of continuity of the $r$-th derivative of the function f are calculated.

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