The exact Jackson–Stechkin inequality in L2,μα
Точное неравенство Джексона — Стечкина в L2,μα
Tileubayev T.E.
2023State Lev Tolstoy Pedagogical University
Chebyshevskii Sbornik
2023#24Issue 3139 - 161 pp.
Several extremal problems on the best mean-square approximation of the functions f, on a semiaxis with a power-law weight are solved in the paper, which can be applied in solving various problems. Exact Jackson–Stechkin-type inequalities are obtained for some classes of functions in which the values of the best approximations are estimated from above in terms of k-th order Hankel moduli of smoothness.
best approximation , exact constants. Bibliography: 36 titles , Jackson inequality , moduli of smoothness
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Eurasian L. N. Gumilyov National University, Astana, Kazakhstan
Eurasian L. N. Gumilyov National University
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