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Part of the book series: Studies in Computational Intelligence ((SCI,volume 734))

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Abstract

Here we study quantitatively the rate of convergence of sequences of linear operators acting on Banach space valued continuous functions to the unit operator.

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References

  1. G.A. Anastassiou, Moments in Probability and Approximation Theory, Pitman Research Notes in Math, vol. 287 (Longman Science and Technology, Harlow, U.K., 1993)

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  2. G.A. Anastassiou, Lattice homomorphism—Korovkin type inequalities for vector valued functions. Hokkaido Math. J. 26, 337–364 (1997)

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  3. G.A. Anastassiou, Korovkin theory for Banach space valued functions, (submitted for publication, 2017)

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  4. P.P. Korovkin, Linear Operators and Approximation Theory (Hindustan Publishing Corporation, Delhi, India, 1960)

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  5. O. Shisha, B. Mond, The degree of convergence of sequences of linear positive operators. Nat. Acad. Sci. U.S. 60, 1196–1200 (1968)

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Correspondence to George A. Anastassiou .

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Anastassiou, G.A. (2018). Basic Abstract Korovkin Theory. In: Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations. Studies in Computational Intelligence, vol 734. Springer, Cham. https://doi.org/10.1007/978-3-319-66936-6_6

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  • DOI: https://doi.org/10.1007/978-3-319-66936-6_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66935-9

  • Online ISBN: 978-3-319-66936-6

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