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A-Statistical \(L_{p}\) approximation properties of an integral variant of a general positive linear operators

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Abstract

The present paper deals with the A-statistical approximation processes of the general class of integral type linear positive operators including many well-known operators in the \(L_{p}\)-metric spaces.

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References

  1. Agratini, O.: Korovkin type error estimates for Meyer-K önig and Zeller operators. Math. Ineq. Appl. 4(1), 119–126 (2001)

    MATH  Google Scholar 

  2. Altomore, F., Campiti, M.: Korovkin Type Approximation Theory and its Applications. Walter de Gruyter, Berlin (1994)

    Book  Google Scholar 

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

    Book  MATH  Google Scholar 

  4. Bleimann, G., Butzer, P.L., Hahn, L.: A Bernstein-type operator approximating continuous functions on the semi-axis. Indag. Math. 42, 255–262 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  5. Canatan, R., Doğru, O.: Statistical approximation properties of a generalization of positive linear operators. Eur. J. Pure Appl. Math 5(1), 75–87 (2012)

    MathSciNet  MATH  Google Scholar 

  6. Cheney, E.W., Sharma, A.: Bernstein power series. Can. J. Math. 16, 241–253 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  7. Doğru, O.: Necessary conditions to obtain Voronovskaja type asymptotic formlae via statistical limit, Proc. of the 12th WSEAS Int. Conf. on Applied Mathematics, Cairo, Egypt, Dec. 29–31, pp. 128-131 (2007)

  8. Doğru, O.: Approximation properties of a generalization of positive linear operators. J. Math. Anal. Appl. 342, 161–170 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Doğru, O., Özalp, N.: Approximation by Kantorovich type generalization of Meyer-König and Zeller operators. Glasnik Math. 36(56), 311–318 (2001)

    MATH  Google Scholar 

  10. Doğru, O., Duman, O., Orhan, C.: Statistical approximation by generalized Meyer-König and Zeller operators. Stud. Sci. Math. Hung. 40, 359–371 (2003)

    MATH  Google Scholar 

  11. Duman, O., Khan, M.K., Orhan, C.: $A-$Statistical convergence of approximating operators. Math. Inequal. Appl. 6(4), 689–699 (2003)

    MathSciNet  MATH  Google Scholar 

  12. Dzyadik, V.K.: On the approximation of functions by linear positive operators and singular integrals. Mat. Sb. 70, 508–517 (1966). (in Russian)

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Freedman, A.R., Semberm, Jj: Densities and summability. Pac. J. Math. 95, 293–305 (1981)

    Article  MathSciNet  Google Scholar 

  15. Fridy, J.A.: On statistical convergence. Analysis 5, 301–313 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fridy, J.A., Miller, H.I.: A matrix characterization of statistical convergence. Analysis 11, 59–66 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  17. Fridy, J.A., Orhan, C.: Statistical limit superior and limit inferior. Proc. Am. Math. Soc. 125, 3625–3631 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Gadjiev, A.D., Orhan, C.: Some approximation theorems via statistical convergence. Rocky Mount. J. Math. 32, 129–138 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gonska, H., Badea, C., Badea, I.: A test function theorem and approximation by pseudopolynomials. Bull. Austral. Math. Soc. 34, 53–64 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hardy, G.H.: Divergent Series. Oxford Univ. Press, London (1949)

    MATH  Google Scholar 

  21. Khan, M.K.: On the rate of convergence of Bernstein power series for functions of bounded variation. J. Approx. Theory 57(1), 90–103 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  22. Kolk, E.: Matrix summability of statistically convergent sequences. Analysis 13, 77–83 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  23. Miller, H.I.: A measure theoretical subsequence characterization of statistical convergence. Trans. Am. Math. Soc. 347, 1811–1819 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  24. Szász, O.: Generalization of S. Bernstein’s polynomials to the infinite interval. J. Res. Nat. Bur. Stand. 45, 239–245 (1950)

    Article  MathSciNet  Google Scholar 

  25. Totik, V.: Approximation by Meyer-König and Zeller type operators. Math. Z. 182, 425–446 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  26. Volkov, V.: On the convergence sequences of linear positive operators in the space of continuous functions of two variables. Dokl. Akad. Nauk. SSSR (N.S.) 115, 17–19 (1957). (Russian)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Pre- and In-Service Teacher Training Department, Faculty of Sciences, “Vasile Alecsandri” University of Bacau, Bacau, Romania

    Carmen Muraru

  2. Department of Mathematics, Faculty of Science, Gazi University, Ankara, Turkey

    Ogün Doğru & Aslıhan Gülsün

Authors
  1. Carmen Muraru
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  2. Ogün Doğru
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  3. Aslıhan Gülsün
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Correspondence to Carmen Muraru.

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Communicated by Javier Soria.

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Muraru, C., Doğru, O. & Gülsün, A. A-Statistical \(L_{p}\) approximation properties of an integral variant of a general positive linear operators. Ann. Funct. Anal. 11, 761–779 (2020). https://doi.org/10.1007/s43034-020-00053-1

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  • DOI: https://doi.org/10.1007/s43034-020-00053-1

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