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k-Snakes in finite-order interpolational classes of functions

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Ukrainian Mathematical Journal Aims and scope

Abstract

k-snakes are a generalization of the polynomials with the least deviation from zero underk-constraints. We prove the existence and uniqueness ofk-snakes in finite-order interpolational classes and their continuous differentiability with respect to a parameter.

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References

  1. V. I. Morozov, “On some questions of uniform approximation of functions of interpolational classes,“Izv. Akad. Nauk SSSR, Ser. Mat.,16, No. 1, 75–100 (1952).

    Google Scholar 

  2. Ya. G. Ivashchuk, “A theorem of the existence of 2-snakes for finite-order interpolational classes,“ in:Investigations in the Theory of Approximation of Functions [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, (1991), pp. 38–44.

    Google Scholar 

  3. V. K. Dzyadyk,Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  4. V. V. Kovtunets, “k-snakes as a generalization of polynomials with the least deviation from zero under constraints,“Izv. Akad. Nauk SSSR, Ser. Mat.,45, No. 4, 905–925 (1981).

    Google Scholar 

  5. V. V. Kovtunets, “Parametric differentiation of a family ofk-snakes,“Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 7, 12–15 (1982).

    Google Scholar 

  6. V. N. Burov, “On some questions of uniform approximations of functions,“Uchen. Zapiski Leningrad. Polytechnich. Inst.,218, 127–140 (1961).

    Google Scholar 

  7. N. V. Didkovskaya, On Uniform Continuity of Nonlinear Chebyshev Best Approximating Operator for Interpolational Classes [in Russian], Deposited in VINITI No. 2684, Leningrad (1983).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    Ya. G. Ivashchuk

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  1. Ya. G. Ivashchuk
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 2, pp. 243–250, February, 1993.

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Ivashchuk, Y.G. k-Snakes in finite-order interpolational classes of functions. Ukr Math J 45, 260–268 (1993). https://doi.org/10.1007/BF01060982

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  • DOI: https://doi.org/10.1007/BF01060982

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