Kyungpook Mathematical Journal

  • 제46권2호
  • /
  • Pages.185-188
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  • 2006
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

Durrmyer Type Summation Integral Operators

  • Kumar, Niraj (School of Applied Sciences, Netaji Subhas Institute of Technology)
  • 투고 : 2004.05.31
  • 발행 : 2006.06.23
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초록

In the present paper, we give the applications of the optimum bound for Bernstein basis functions. It is noted that using the optimum bound the main results of Aniol and Taberska [Ann. Soc. Math. Pol. Seri, Commentat. Math., 30(1990), 9-17], [Approx. Theory and its Appl. 11:2(1995), 94-105] and V. Gupta [Soochow J. Math., 23(1)(1997) 115-118] can be improved which were not pointed out earlier.

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참고문헌

  1. G. Aniol and P. Pych Taberska, On the rate of convergence of Durrmeyer polynomials, Ann. Soc. Math. Pol. Seri. Commentat. Math., 30(1990), 9-17.
  2. G. Aniol and P. Pych Taberska, On the rate of point wise convergence of the Durrmeyer type operators, Approx. Theory and its Appl., 11(2)(1995), 94-105.
  3. G. Bastien and M. Rogalski, Convexite, complete monotonie integralites sur les functions zeta et gamma, sur les functions des operateurs be Baskakov et sur des functions arthematiques, Canadian J. Math., 54(5)(2002), 916-944. https://doi.org/10.4153/CJM-2002-034-7
  4. J. L. Durrmeyer, Une Formula d' inversion de la Transformee de Laplace: Application a la Theorie des Moments, These de 3c cycle, Faculte des science de l' university de Paris, 1967.
  5. S. Guo, On the rate of convergence of Durrmeyer operator for functions of bounded variation, J. Approx. Theory, 51(1987), 183-192. https://doi.org/10.1016/0021-9045(87)90033-5
  6. Vijay Gupta, A note on the rate of convergence of Durrmeyer type operators for functions of bounded variation, Soochow J. Math., 23(1)(1997), 115-118.
  7. F. Herzog and J. D. Hill, The Bernstein polynomials of discontinuous functions, Amer. Math. J., 68(1946), 109-112. https://doi.org/10.2307/2371744