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On statistical approximation properties of modified q-Bernstein-Schurer Operators

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In this paper, a kind of modified q-Bernstein-Schurer operators is introduced. The Korovkin type statistical approximation property of these operators is investigated. Then the rates of statistical convergence of these operators are also studied by means of modulus of continuity and the help of functions of the Lipschitz class. Furthermore, a Voronovskaja type result for these operators is given.

Abstract

In this paper, a kind of modified q-Bernstein-Schurer operators is introduced. The Korovkin type statistical approximation property of these operators is investigated. Then the rates of statistical convergence of these operators are also studied by means of modulus of continuity and the help of functions of the Lipschitz class. Furthermore, a Voronovskaja type result for these operators is given.

참고문헌 (14)

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  9. V. G. Kac, "Quantum Calculus, Universitext" (2002), Springer-Verlag
  10. C. V. Muraru, "Note on q-Bernstein-Schurer operators", Stud. Univ. Babes-Bolyai Math, 56(2), pp.480~495 (2011)
  11. I. Niven, "An Introduction to the Theory Numbers, 5th ed" (1991), Wiley
  12. M. Orkcu, "Weighted statistical approximation by Kantorovich type q- Szasz-Mirakjan operators", Appl. Math. Comput, 217(20), pp.7913~7919 (2011)
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  14. Linear positive operators in approximation theory, "F. Schurer", Math. Inst. Techn. Univ, ~ (1962)

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