Self Adjoint Operator Korovkin type Quantitative Approximations
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Abstract
Here we present self adjoint operator Korovkin type theorems, via self adjoint operator Shisha-Mond type inequalities. This is a quantitative treatment to determine the degree of self adjoint operator uniform approximation with rates, of sequences of self adjoint operator positive linear operators. We give several applications involving the self adjoint operator Bernstein polynomials. This study appears for the rst time in the literature.
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Anastassiou, G.
(2017).
Self Adjoint Operator Korovkin type Quantitative Approximations.
Acta Mathematica Universitatis Comenianae, 86(1), 165-186.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/437/423
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References
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No. 287, John Wiley & Sons, Inc., Essex, New York, 1993.
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[4] S. Dragomir, Operator inequalities of Ostrowski and Trapezoidal type, Springer, New York, 2012.
[5] G. Helmberg, Introduction to Spectral Theory in Hilbert Space, John Wiley & Sons, Inc., New York, 1969.
[6] T. Furuta, J. Mi´ci´c Hot, J. Peµcari´c and Y. Seo, Mond-Peµcaric Method in Operator Inequalities. Inequalities for Bounded Selfadjoint Operators on a Hilbert Space, Element, Zagreb, 2005.
[7] C.A. McCarthy, cp, Israel J. Math., 5 (1967), 249-271.
[8] O. Shisha and B. Mond, The degree of convergence of sequences of linear positive operators, Nat. Acad. of Sci. U.S., 60 (1968), 1196-1200.
[9] L. Shumaker, Spline functions basic theory, Wiley-Interscience, New York, 1981