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On the reconstruction via Urysohn-Chlodovsky operators

   | Dec 31, 2020

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[1] U. Abel, H. Karsli, Asymptotic expansions for Bernstein-Durrmeyer-Chlodovsky polynomials, Results Math, 73:104, 2018, 12 pages, https://doi.org/10.1007/s00025-018-0863-0.10.1007/s00025-018-0863-0Search in Google Scholar

[2] U. Abel, H. Karsli, A complete asymptotic expansion for Bernstein-Chlodovsky polynomials for functions on ℝ,, Mediterranean Journal of Mathematics, 2020 accepted.10.1007/s00009-020-01632-1Search in Google Scholar

[3] F. Altomare, M. Campiti, Korovkin-Type Approximation Theory and its Applications, De Gruyter Studies in Mathematics, Walter de Gruyter and Co., Berlin, 17, 1994.10.1515/9783110884586Search in Google Scholar

[4] C. Bardaro, J. Musielak, G. Vinti, Nonlinear Integral Operators and Applications, De Gruyter Series in Nonlinear Analysis and Applications, vol. 9, 2003.10.1515/9783110199277Search in Google Scholar

[5] P. L. Butzer, On Bernstein Polynomials, Ph.D. Thesis, University of Toronto, 1951.Search in Google Scholar

[6] P. L. Butzer, On two dimensional Bernstein polynomials, Canad. J. Math., vol. 5, 1953, 107-113.10.4153/CJM-1953-014-2Search in Google Scholar

[7] P. L. Butzer, H. Karsli, Voronovskaya-type theorems for derivatives of the Bernstein-Chlodovsky polynomials and the Szasz-Mirakyan operator, Comment. Math., vol. 49, 2009, 33-58.Search in Google Scholar

[8] P. L. Butzer, R. J. Nessel, Fourier Analysis and Approximation, Academic Press, New York, London, 1971.10.1007/978-3-0348-7448-9Search in Google Scholar

[9] I. Chlodowsky, Sur le développement des fonctions définies dans un intervalle infini en séries de polynomes de M. S. Bernstein, Compositio Math., vol. 4, 1937, 380-393.Search in Google Scholar

[10] I. I. Demkiv, On Approximation of the Urysohn operator by Bernstein type operator polynomials, Visn. L’viv. Univ., Ser. Prykl. Mat. Inform., no. 2, 2000, 26 - 30.Search in Google Scholar

[11] H. Karsli, Recent results on Chlodovsky operators, Stud. Univ. Babeş-Bolyai Math., vol. 56, no. 2, 2011, 423-436.Search in Google Scholar

[12] H. Karsli, Approximation by Urysohn type Meyer-König and Zeller operators to Urysohn integral operators, Results Math., vol. 72, no. 3, 2017, 1571-1583.10.1007/s00025-017-0729-xSearch in Google Scholar

[13] H. Karsli, Approximation results for Urysohn type nonlinear Bernstein operators, Advances in Summability and Approximation Theory, Springer, Singapore, 2018, 223-241.10.1007/978-981-13-3077-3_14Search in Google Scholar

[14] H. Karsli, Voronovskaya-type theorems for Urysohn type nonlinear Bernstein operators, Math. Methods Appl. Sci., vol. 42, no. 16, 2019, 5190-5198.10.1002/mma.5261Search in Google Scholar

[15] H. Karsli, Approximation Results for Urysohn Type Two Dimensional Nonlinear Bernstein Operators, Const. Math. Anal., vol. 1, no. 1, 2018, 45-57.10.33205/cma.453027Search in Google Scholar

[16] H. Karsli, Some Approximation Properties of Urysohn type nonlinear operators, Stud. Univ. Babes-Bolyai Math., vol. 64, no. 2, 2019, 183-196.10.24193/subbmath.2019.2.05Search in Google Scholar

[17] H. Karsli, On Urysohn type Generalized Sampling Operators, Dolomites Research Notes on Approximation, 2020, accepted.10.3934/mfc.2021015Search in Google Scholar

[18] G. G. Lorentz, Bernstein Polynomials, University of Toronto Press, Toronto, 1953.Search in Google Scholar

[19] V. L. Makarov, I. I. Demkiv, Approximation of the Urysohn operator by operator polynomials of Stancu type, Ukrainian Math Journal, vol. 64, no. 3, 2012, 356-386.10.1007/s11253-012-0652-ySearch in Google Scholar

[20] V. L. Makarov, V. V. Khlobystov, Interpolation method for the solution of identification problems for a functional system described by the Urysohn operator, Dokl. Akad. Nauk SSSR, vol. 300, no. 6, 1988, 1332-1336.Search in Google Scholar

[21] A. D. Polyanin, A. V. Manzhirov, Handbook of Integral Equations, 2nd ed., Chapman and Hall/CRC Press, 2008.10.1201/9781420010558Search in Google Scholar

[22] P. Urysohn, Sur une classe d’equations integrales non lineaires, Mat. Sb., vol. 31, 1923, 236-255.Search in Google Scholar

[23] P. Urysohn, On a type of nonlinear integral equation, Mat. Sb., vol. 31, 1924, 236-355.Search in Google Scholar

[24] A. M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications, Beijing and Springer-Verlag Berlin, Higher Education press, 2011.Search in Google Scholar

[25] P. P. Zabreiko, A. I. Koshelev, M. A. Krasnosel’skii, S. G. Mikhlin, L. S. Rakovscik, V. Ja. Stetsenko, Integral Equations: A Reference Text, Noordhoff Int. Publ., Leyden, 1975.Search in Google Scholar