On one property of the modulus of continuity for periodic functions of higher orders

Authors

  • Yu. A. Maksymenkova Institute Of Industrial And Business Technologies Ukrainian State University Of Science And Technologies
  • Т. F. Michaylova Institute Of Industrial And Business Technologies Ukrainian State University Of Science And Technologies

DOI:

https://doi.org/10.37863/umzh.v74i8.7217

Keywords:

модуль неперервності, кратні модулі неперервності

Abstract

UDC 517.5

For the moduli of continuity of 2π-periodic functions ωk(f,h) of order k=1,2,, we prove the inequalities
ωk(f,π)2kC[k2]k1ππ0ωk(f,h)dh,
for even k.
The inequalities are exact in the spaces C2π and L1[π,π].

Author Biography

  • Т. F. Michaylova , Institute Of Industrial And Business Technologies Ukrainian State University Of Science And Technologies

     

     

References

S. M. Nikol'skij, Ryad Fur'e funkcij s dannym modulem nepreryvnosti, Dokl. AN SSSR, 52, 191 – 193 (1946).

V. A. YUdin, O module nepreryvnosti v L2, Sib. mat. zhurn., 20, 449 – 450 (1979). DOI: https://doi.org/10.1007/BF00970049

S. V. Konyagin, O modulyah nepreryvnosti funkcij, Tez. dokl. Vsesoyuz. shkoly po teorii funkcij (Kemerovo, 1983) (1983), s. 59.

V. I. Ivanov, O module nepreryvnosti v Lp, Mat. zametki, 41, № 5, 682 – 686 (1987).

N. M. Ryzhik, I. S. Gradshtejn, Tablicy integralov, summ, ryadov i proizvedenij, Gostekhteorizdat, Moskva (1951).

Published

04.10.2022

Issue

Section

Short communications

How to Cite

Maksymenkova , Yu. A., and Michaylova Т. F. “On One Property of the Modulus of Continuity for Periodic Functions of Higher Orders ”. Ukrains’kyi Matematychnyi Zhurnal, vol. 74, no. 8, Oct. 2022, pp. 1149-52, https://doi.org/10.37863/umzh.v74i8.7217.