Saturation results for the Lagrange max-product interpolation operator based on equidistant knots

Lucian Coroianu; Sorin G. Gal

doi:10.33993/jnaat411-966

Authors

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

DOI:

https://doi.org/10.33993/jnaat411-966

Keywords:

Lagrange max-product interpolation operator, saturation order, local inverse result

Abstract views: 230

Abstract

In this paper we obtain the saturation order and a local inverse result in the approximation by the Lagrange max-product interpolation operator based on equidistant knots.

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References

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

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

B. Bede, L. Coroianu and S.G. Gal, Approximation by truncated Favard-Szász-Mirakjan operator of max-product kind, Demonstratio Mathematica, XLIV, no. 1, pp. 105-122, 2011, https://doi.org/10.1515/dema-2013-0300 DOI: https://doi.org/10.1515/dema-2013-0300

B. Bede, L. Coroianu and S.G. Gal, 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.

B. Bede, L. Coroianu and S.G. Gal Approximation and shape preserving properties of the nonlinear Meyer-Konig and Zeller operator of max-product kind, Numerical Functional Analysis and Optimization, 31, no. 3, pp. 232-253, 2010. https://doi.org/10.1080/01630561003757686 DOI: https://doi.org/10.1080/01630561003757686

B. Bede, L. Coroianu and S.G. Gal, Approximation and shape preserving properties of the truncated Baskakov operator of max-product kind, Revista de la Union Matematica Argentina, 52, no. 1, pp. 89-107, 2011.

B. Bede, L. Coroianu and S.G. Gal, 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. DOI: https://doi.org/10.2298/FIL1003055B

S. Bernstein, Quelques remarques sur l'interpolation, Math. Ann., 79, no.1-2, pp. 1-12, 1918. https://doi.org/10.1007/bf01457173 DOI: https://doi.org/10.1007/BF01457173

E. Borel, Sur l'interpolation, C.R. Acad. Sci. Paris, 124, pp. 673-676, 1897.

S. Cobzas and I. Muntean, Condensation of singularities and divergence results in approximation theory, J. Approx. Theory, 31, no. 2, pp. 138-153, 1980. https://doi.org/10.1016/0021-9045(81)90038-1 DOI: https://doi.org/10.1016/0021-9045(81)90038-1

L. Coroianu and S.G. Gal, Approximation by nonlinear Lagrange interpolation operators of max-product kind on Chebyshev knots of second kind, J. Comp. Anal. Appl., 13, no. 2, pp. 211-224, 2010.

L. Coroianu and S.G. Gal, Approximation by nonlinear Hermite-Fejér interpolation operators of max-product kind on Chebyshev nodes, Revue d'Anal. Numér. Théor. Approx. (Cluj), 39, no.1, pp. 29-39, 2010, http://ictp.acad.ro/jnaat/journal/article/view/2010-vol39-no1-art3

L. Coroianu and S.G. Gal, Approximation by max-product Lagrange interpolation operators, Studia Univ. "Babeş-Bolyai", ser. Math., LVI, no. 2, pp. 1-11, 2011.

L. Coroianu and S.G. Gal, Classes of functions with improved estimates in approximation by the max-product Bernstein operator, Analysis and Applications, 9, no. 3, pp. 249-274, 2011. https://doi.org/10.1142/s0219530511001856 DOI: https://doi.org/10.1142/S0219530511001856

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

I. Muntean, The Lagrange interpolation operators are densely divergent, Studia Univ. "Babes-Bolyai" (Cluj), ser. math. 21, pp. 28-30, 1976.

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