Article
Article name About Extremal Problem of Approximation Theory
Authors Abakumov Y.G. Candidate of Physics and Mathematics, abakumovug@yandex.ru
Batyrova , , Chita State University (), e-mail: chita82renata@mail.ru R.. Assistant teacher thr of Department of Mathematics, hita82renata@mail.ru
Verkhoturova M.. Assistant teacher of Department of Mathematics, mar-verhoturova@yandex.ru
Kogan Y.S. Candidate of Physics and Mathematics, eskogan@mail.ru
Bibliographic description
Section Scientific Research
UDK УДК 517.51
DOI
Article type
Annotation The article discusses several issues related to the task of finding the constants A[m](k1,...,km) H = limn→∞nsup M [ m](k1,...,km) n (f, x) − f(x) , , where M[m](k1,...,km) n are trigonometric operators of Baskakov. The constants A[m](k1,...,km) n are called the exact constants. The article provides an overview of the results obtained earlier by the authors, full proofs of results that were previously announced. We give a complete solution of the problem, as well as m = 1, 2, 3, as well as m = 4,if (k1, k2, k3, k4) = (1, 2, 3, 4), (k1, k2, k3, k4) = (1, 2, 3, 5), (k1, k2, k3, k4) = (1, 2, 4, 5), п as m = 5, (k1, k2, k3, k4, k5) = (1, 2, 3, 4, 5). We also investigate the dynamics of change in value of the constant A[1](k) H the growth parameter k.
Key words trigonometric operators of Baskakov,exact constant
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