Stechkin-type estimate for nearly copositive approximation of periodic functions

Authors

  • G. A. Dzyubenko Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv

DOI:

https://doi.org/10.37863/umzh.v72i5.1127

Abstract

Under the conditions that a continuous 2π-periodic function f on the real axis changes its sign at 2s points yi:πy2s<y2s1<<y1<π, sN, the other points yi, iZ, are defined by periodicity, and natural n>N(k,yi), where N(k,yi) is a constant that depends only on kN and mini=1,,2s{yiyi+1}, we find a trigonometric polynomial Pn of order n such that the signs of Pn and f are the same everywhere with the possible exception for small neighborhoods of the points yi:(yiπ/n,yi+π/n), Pn(yi)=0, iZ, and where c(k,s) is a constant that depends only on k and s; \omega_k(f,\cdot) is the kth modulus of smoothness of f, and \|\cdot\| is the max-norm.

References

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Published

29.04.2020

Issue

Section

Research articles

How to Cite

Dzyubenko, G. A. “Stechkin-Type Estimate for Nearly Copositive Approximation of Periodic Functions”. Ukrains’kyi Matematychnyi Zhurnal, vol. 72, no. 5, Apr. 2020, pp. 628–634, https://doi.org/10.37863/umzh.v72i5.1127.