Approximation by nonlinear Hermite-Fejer interpolation operators of max-product kind on Chebyshev nodes

Lucian Coroianu; Sorin G. Gal

doi:10.33993/jnaat391-917

Authors

Lucian Coroianu University of Oradea, Romania
Sorin G. Gal University of Oradea, Romania

DOI:

https://doi.org/10.33993/jnaat391-917

Keywords:

nonlinear Hermite-Fejer interpolation operators of max-product kind, Chebyshev nodes of first kind, degree of approximation

Abstract views: 311

Abstract

The aim of this note is that by using the so-called max-product method, to associate to the Hermite-Fejer polynomials based on the Chebyshev knots of first kind, a new interpolation operator for which a Jackson-type approximation order in terms of \(\omega_{1}(f; 1/n)\) is obtained.

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References

Bede, B. and Gal, S.G., Approximation by nonlinear Bernstein and Favard-Szász-Mirakjan operators of max-product kind, Journal of Concrete and Applicable Mathematics, 8, No. 2, pp. 193-207, 2010.

Bede, B., Coroianu, L. and Gal, S.G., Approximation and shape preserving properties of the Bernstein operator of max-product kind, Intern. J. Math. and Math. Sci., volume 2009, Article ID 590589, 26 pages, doi:10.1155/2009/590589. DOI: https://doi.org/10.1155/2009/590589

Bede, B., Coroianu, L. and Gal, S.G., Approximation by truncated nonlinear Favard-Szász-Mirakjan operators of max-product kind, Demonstratio Mathematica, (accepted for publication).

Bede, B., Coroianu, L. and Gal, S.G., Approximation and shape preserving properties of the nonlinear Baskakov operator of max-product kind, Studia Univ. "Babeş-Bolyai", Ser. Math., LV, pp. 193-218, 2010.

Bede, B., Coroianu, L. and Gal, S.G., Approximation and shape preserving properties of the nonlinear Bleimann-Butzer-Hahn operators of max-product kind, Comment. Math. Univ. Carol., 51 no. 3, pp. 397-415, 2010. DOI: https://doi.org/10.2298/FIL1003055B

Bojanic, R., A note on the precision of interpolation by Hermite-Fejér polynomials, Proceedings of the Conference on the Constructive Theory of Functions (Approximation Theory) (Budapest, 1969), pp. 69-76, Akadémiai Kiadó, Budapest, 1972.

Fejér, L., Über Interpolation, Göttingen Nachrichten, pp. 66-91, 1916. DOI: https://doi.org/10.1515/crll.1916.146.53

Gal, S.G., Shape-Preserving Approximation by Real and Complex Polynomials, Birkhäuser, Boston-Basel-Berlin, 2008. DOI: https://doi.org/10.1007/978-0-8176-4703-2

Hermann, T. and Vértesi, P., On the method of Somorjai, Acta Math. Hung., 54(3-4), pp. 253-262, 1989, https://doi.org/10.1007/bf01952055 DOI: https://doi.org/10.1007/BF01952055

Lorentz, G.G., Aproximation of Functions, Chelsea Publ. New York, 1987.

Moldovan, E., Observations sur certains procédés d'interpolation généralisés (Romanian, Russian and French summaries) Acad. Repub. Pop. Romane, Bul. Stiint., Sect. Stiint. Mat. Fiz. 6, pp. 477-482, 1954,

Popoviciu, T., On the proof of Weierstrass' theorem with the interpolation polynomials (in Romanian), Acad. Repub. Pop. Romane, "Lucrarile sesiunii generale stiintifice din 2-12 Iunie 1950", pp. 1664-1667, 1951.

Prasad, J., On the degree of approximation of the Hermite and Hermite-Fejér interpolation, Internat. J. Math. and Math. Sci., 15, No. 1, pp. 47-56, 1992, https://doi.org/10.1155/s0161171292000061 DOI: https://doi.org/10.1155/S0161171292000061

Szabados, J. and Vértesi, P., Interpolation of Functions, World Scientific, Singapore, New Jersey, London, Hong Kong, 1990. DOI: https://doi.org/10.1142/0861

Szabados, J., On the convergence and saturation problem of the Jackson polynomials, Acta Math. Acad. Sci. Hung., 24(3-4), pp. 399-406, 1973, https://doi.org/10.1007/bf01958053 DOI: https://doi.org/10.1007/BF01958053

Vértesi, P., On the convergence of Hermite-Fejér interpolation, Acta Math. Acad. Sci. Hung., 22, pp. 151-158, 1971, https://doi.org/10.1007/bf01896002 DOI: https://doi.org/10.1007/BF01896002

Xie Hua Sun and Jiang Dechang, On the convergence rate of Hermite-Fejér interpolation at zeros of Jacobi polynomials, Soochow Journal of Mathematics, 23, No. 3, pp. 293-304, 1997.