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On Some Conditions for the Second Moduli of Continuity

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Ukrainian Mathematical Journal Aims and scope

We study the second moduli of continuity for functions from the space of continuous and periodic real functions and the space of functions uniformly continuous on the entire axis. In both spaces, we give negative answer to the question about the necessity of a condition formulated by V. E. Geit, which is sufficient for a function to be the second module of continuity.

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References

  1. I. A. Shevchuk, Approximation by Polynomials and Traces of Functions Continuous on a Segment [in Russian], Naukova Dumka, Kiev (1992).

  2. I. A. Shevchuk, “Some remarks on functions of the type of modulus of continuity of order k ≥ 2,” in: Problems of the Theory of Approximation of Functions and Its Applications [in Russian], Institute of Mathematics, Academy of Science of Ukr. SSR, Kiev (1976), pp. 194–199.

  3. V. É Geit, “Embedding theorems for some classes of periodic continuous functions,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 4, 67–77 (1972).

  4. V. É Geit, “On the functions that are second moduli of continuity,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 9, 38–41 (1998).

  5. S. V. Konyagin, “On the second moduli of continuity,” in: Theory of Functions and Differential Equations [in Russian], Tr. Mat. Inst. Akad. Nauk, 269 (2010), pp. 150–152.

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Authors and Affiliations

  1. T. Shevchenko Kyiv National University, Kyiv, Ukraine

    A. V. Chaikovs’kyi

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  1. A. V. Chaikovs’kyi
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Correspondence to A. V. Chaikovs’kyi.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 9, pp. 1291–1296, September, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i9.7068.

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Chaikovs’kyi, A.V. On Some Conditions for the Second Moduli of Continuity. Ukr Math J 74, 1471–1477 (2023). https://doi.org/10.1007/s11253-023-02148-z

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  • DOI: https://doi.org/10.1007/s11253-023-02148-z

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