Jackson-Type Inequalities in the Space Sp
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In the case of approximation of periodic functions in the space Sp, we determine the exact constants in Jackson-type inequalities for the Zygmund, Rogosinski, and de la Valleé Poussin linear summation methods.
KeywordsPeriodic Function Summation Method Linear Summation Exact Constant Linear Summation Method
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- 1.A. I. Stepanets, “Approximation characteristics of the spaces S fp,” Ukr. Mat. Zh., 53, No. 3, 392–417 (2001).Google Scholar
- 2.A. I. Stepanets, “Approximation characteristics of the spaces S fp in different metrics,” Ukr. Mat. Zh., 53, No. 8, 1121-1147 (2001).Google Scholar
- 3.A.I. Stepanets and A. S. Serdyuk, “Direct and inverse theorems in the theory of approximation of functions in the space S p,” Ukr. Mat. Zh., 54, No. 1, 106-124 (2002).Google Scholar
- 4.A. A. Ligun, “Some inequalities for the best approximation and modulus of continuity in the space L 2,” Mat. Zametki, 24, No. 6, 785-792(1978Google Scholar
- 5.N. Bozhukha “Inequalities of the Jackson type in the approximation of periodic functions by Fejér, Rogosinski, and Korovkin polynomials,” Ukr. Mat. Zh., 52, No. 12, 1596-1602 (2000).Google Scholar
- 6.V. R. Voitsekhivs'kyi, “Jackson-type inequalities in the approximation of functions from the space S p by Zygmund sums,” in: Theory of Approximation of Functions and Related Problems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002), pp. 33-46.Google Scholar
- 7.N. I. Chernykh, “On the Jackson inequality in L 2,” Tr. Mat. Inst. Akad. Nauk SSSR, 88, 71-74 (1967).Google Scholar
- 8.N. I. Chernykh, “On the best approximation of periodic functions by trigonometric polynomials in L 2,” Mat. Zametki, 2, No. 5, 513-522 (1967).Google Scholar
- 9.L. V. Taikov, “Inequalities containing best approximations and modulus of continuity from L 2,” Mat. Zametki, 20, No. 3, 433-438 (1976).Google Scholar