Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Khromova G. V. On Operators with Discontinuous Range. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 3, pp. 298-302. DOI: 10.18500/1816-9791-2016-16-3-298-302, EDN: RZLWFV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.09.2016
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Language: 
Russian
Heading: 
Mathematics
UDC: 
517.51
DOI: 
10.18500/1816-9791-2016-16-3-298-302
EDN: 
RZLWFV

On Operators with Discontinuous Range

Autors: 
Khromova Galina Vladimirovna, Saratov State University
Abstract: 

With the use of operators from approximation function theory we construct integral operators with discontinuous range of values, which make it possible to obtain uniform approximations of continuous functions on the whole interval of their definition. 

Key words: 
Operator
continuous function
interval
uniform approximations
References: 
  1. Goncharov V. L. The theory of interpolation and approximation of functions. Moscow, GITL, 1954 (in Russian).
  2. Khromova G. V. The problem of the reconstruction of functions that are given with error. U.S.S.R. Comput. Math. Math. Phys., 1977, vol. 17, no. 5, pp. 1161–1171.
  3. Sendov B. X. A modified Steklov function. C. R. Acad. Bulg. Sci., 1983, vol. 134, no. 2, pp. 355– 379.
  4. Khromov A. P., Khromova G. V. On a modification of the Steklov operator. Modern Problems in Function Theory and Applications : Abstracts of Papers of Saratov Winter School, Saratov, Saratov Univ. Press, 2010, pp. 181 (in Russian).
  5. Khromov A. P., Khromova G. V. A family of operators with discontinuous ranges and approximation and restoration of continuous functions. Comput. Math. Math. Phys., 2013, vol. 53, no. 10, pp. 1603– 1609. DOI: https://doi.org/10.1134/S0965542513100096.
  6. Khromov A. P., Khromova G. V. Discontinuous Steklov operators in the problem of uniform approximation of derivatives on an interval. Comput. Math. Math. Phys., 2014, vol. 54, no. 9, pp. 57–62. DOI: https://doi.org/10.1134/S0965542514090085.
  7. Khromov A.A., Khromova G. V. The solution of the problem of determining the density of heat sources in a rod, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2015, vol. 15, no. 3, pp. 309–314. DOI: https://doi.org/10.18500/1816-9791-2015-15-3-309-314.
  8. Khromova G. V. Regularization of Abel Equation with the Use of Discontinuous Steklov Operator, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2014, vol. 14, no. 4, pp. 597–601.
  9. Khromova G. V. On uniform approximations to the solution of the Abel integral equation. Comput. Math. Math. Phys., 2015, vol. 55, no. 10, pp. 1703– 1712. DOI: https://doi.org/10.1134/S0965542515100139.
  10. Nathanson I. P. Theory of functions of a real variable. St. Petersburg, Lan’, 2013, 560 p. (in Russian).
Received: 
22.04.2016
Accepted: 
26.08.2016
Published: 
30.09.2016
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