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Summation Process by Max-Product Operators

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Computational Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 155))

Abstract

In this study, we focus on the approximation to continuous functions by max-product operators in the sense of summation process. We also study error estimation corresponding to this approximation. At the end, we present an application to max-product Bernstein operators.

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References

  1. F. Altomare, M. Campiti, Korovkin Type Approximation Theory and Its Application (Walter de Gruyter, Berlin, 1994)

    Book  MATH  Google Scholar 

  2. G.A. Anastassiou, O. Duman, Towards Intelligent Modeling: Statistical Approximation Theory. Intelligent Systems Reference Library, vol. 14 (Springer, Berlin, 2011)

    Google Scholar 

  3. G.A. Anastassiou, S.G. Gal, Approximation Theory: Moduli of Continuity and Global Smoothness Preservation (Birkhäuser, Boston, 2000)

    Book  MATH  Google Scholar 

  4. B. Bede, S.G. Gal, Approximation by nonlinear Bernstein and Favard-Szász-Mirakjan operators of max-product kind. J. Concr. Appl. Math. 8, 193–207 (2010)

    MathSciNet  MATH  Google Scholar 

  5. B. Bede, H. Nobuhara, M. Daňková, A. Di Nola, Approximation by pseudo-linear operators. Fuzzy Sets Syst. 159, 804–820 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. B. Bede, E.D. Schwab, H. Nobuhara, I.J. Rudas, Approximation by Shepard type pseudo-linear operators and applications to image processing. Int. J. Approx. Reason. 50, 21–36 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the Bernstein operator of max-product kind. Int. J. Math. Math. Sci. 2009, 26 pp. (2009). Art. ID 590589

    Google Scholar 

  8. B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the nonlinear Baskakov operator of max-product kind. Stud. Univ. Babeş-Bolyai Math. 55, 193–218 (2010)

    MathSciNet  MATH  Google Scholar 

  9. B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the nonlinear Favard-Szász-Mirakjan operator of max-product kind. Filomat 24, 55–72 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the nonlinear Bleimann-Butzer-Hahn operators of max-product kind. Comment. Math. Univ. Carol. 51, 397–415 (2010)

    MathSciNet  MATH  Google Scholar 

  11. B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the nonlinear Meyer-König and Zeller operator of max-product kind. Numer. Funct. Anal. Optim. 31, 232–253 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. B. Bede, L. Coroianu, S.G. Gal, Approximation by truncated Favard-Szász-Mirakjan operator of max-product kind. Demonstratio Math. 44, 105–122 (2011)

    MathSciNet  MATH  Google Scholar 

  13. H.T. Bell, Order summability and almost convergence. Proc. Am. Math. Soc. 38, 548–552 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  14. O. Duman, Statistical convergence of max-product approximating operators. Turk. J. Math. 34, 501–514 (2010)

    MathSciNet  MATH  Google Scholar 

  15. H. Fast, Sur la convergence statistique. Colloq. Math. 2, 241–244 (1951)

    MathSciNet  MATH  Google Scholar 

  16. P.P. Korovkin, Linear Operators and Theory of Approximation (Hindustan Publ. Co, Delhi, 1960)

    MATH  Google Scholar 

  17. G.G. Lorentz, A contribution to the theory of divergent sequences. Acta Math. 80, 167–190 (1948)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Türkan Yeliz Gökçer .

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Gökçer, T.Y., Duman, O. (2016). Summation Process by Max-Product Operators. In: Anastassiou, G., Duman, O. (eds) Computational Analysis. Springer Proceedings in Mathematics & Statistics, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-319-28443-9_4

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