EXACT CONSTANTS IN JACKSON–STECHKIN INEQUALITY IN L2 WITH A POWER-LAW WEIGHT
Точные константы в неравенстве Джексона — Стечкина в L2 со степенным весом.
Tileubayev T.E.
2023Krasovskii Institute of Mathematics and Mechanics
Trudy Instituta Matematiki i Mekhaniki UrO RAN
2023#29Issue 1259 - 279 pp.
In this paper, we have solved several extremal problems of the best mean-square approximation of function f, on the semiaxis with a power-law weight, which can be used to solve various problems. Sharp Jackson–Stechkin type inequalities are obtained on some classes of functions in which the values of the best approximations are estimated from above through moduli of smoothness of the k-th order.
Bessel function , best approximations , exact constants in Jackson–Stechkin inequality , moduli of smoothness
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Faculty of Mechanics and Mathematics L. N. Gumilyov Eurasian National University, 2 Satpaeva st., Astana, 010008, Kazakhstan
Faculty of Mechanics and Mathematics L. N. Gumilyov Eurasian National University
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