Simultaneous approximation by Szász–Mirakjan–Durrmeyer-type operators

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• 作者：Vishnu Narayan Mishra ; R. B. Gandhi…
• 关键词：Durrmeyer operators ; Szász–Mirakjan operators ; Simultaneous approximation ; Modulus of continuity ; 41A10 ; 41A36
• 刊名：Bollettino dell'Unione Matematica Italiana
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：8
• 期：4
• 页码：297-305
• 全文大小：370 KB
• 参考文献：1.Acar, T., Mishra, L.N., Mishra, V.N.: Simultaneous approximation for generalized Srivastava–Gupta operator. J. Funct. Spaces 2015, Article ID 936308. doi:10.​1155/​2015/​936308
  2.Cardenas-Morales, D., Garrancho, P., Rasa, I.: Asymptotic formulae via a Korovkin-type result. Abstr. Appl. Anal. 2012, Article ID 217464
  3.Derriennic, M.M.: Sur I’approximation des fonctions d’une ou plusieurs variables par des polynomes de Bernstein modifiés et application au probléme des moments. Thése de 3e cycle, Université de Rennes (1978)
  4.Durrmeyer, J.L.: Une formule d’inversion de la transformée de Laplace: Applications á la théorie des moments, Thése de 3e cycle, Faculté des Sciences de I’Université de Paris (1967)
  5.Floater, M.S.: On the convergence of derivatives of Bernstein approximation. J. Approx. Theory 134, 130–135 (2005)MATH MathSciNet CrossRef
  6.Gonska, H., Rasa, I.: Asymptotic behaviour of differentiated Bernstein polynomials. Mat. Vesnik 61, 53–60 (2009)MATH MathSciNet
  7.Gonska, H., Heilmann, M., Rasa, I.: Kantorovich operators of order k. Numer. Funct. Anal. Optim. 32, 717–738 (2011)MATH MathSciNet CrossRef
  8.Gupta, V., Aslam Noor, M., Beniwal, M.: On simultaneous approximation for certain Baskakov–Durrmeyer type operators. J. Inequal. Appl Pure Appl. Math. 7, 1–15 (2006)
  9.López-Moreno, A.-J.: Weighted simultaneous approximation with Baskakov type operators. Acta Math. Hung. 104(1), 143–151 (2004)MATH CrossRef
  10.Mazhar, S.M., Totik, V.: Approximation by modified Szász operators. Acta Sci. Math. 49, 257–269 (1985)MATH MathSciNet
  11.Mirakjan, G.M.: Approximation of continuous functions with the aid of polynomials. Dokl. Akad. Nauk SSSR 31, 201–205 (1941)MATH
  12.Mishra, V.N., Khatri, K., Mishra, L.N., Deepmala: Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators. J. Inequal. Appl. 586, 1–11 (2013)
  13.Sahai, A., Prasad, G.: On simultaneous approximation by modified Lupaş operators. J. Approx. Theory 45, 122–128 (1985)MATH MathSciNet CrossRef
  14.Sun, X.: On the simultaneous approximation of functions and their derivatives by the Szász–Mirakjan operators. J. Approx. Theory 55, 279–288 (1988)MATH MathSciNet CrossRef
  15.Szász, O.: Generalization of S. Bernstein’s polynomials to the infinite interval. J. Res. Nat. Bur. Stand. Sect. B 45, 239–245 (1950)CrossRef
  
• 作者单位：Vishnu Narayan Mishra (1) (2)
  R. B. Gandhi (1) (3)
  Fadel Nasaireh (4)
  
  1. Department of Applied Mathematics and Humanities, Sardar Vallabhbhai National Institute of Technology, Ichchhanath Mahadev-Dumas Road, Surat, Gujarat, 395 007, India
  2. L. 1627 Awadh Puri Colony Beniganj, Phase-III, Opposite - Industrial Training Institute (I.T.I.), Ayodhya Main Road, Faizabad, Uttar Pradesh, 224 001, India
  3. Department of Mathematics, BVM Engineering College, Vallabh Vidyanagar, Gujarat, 388 120, India
  4. Mathematics Department, Technical University of Cluj Napoca, Cluj Napoca, Romania
  
• 刊物类别：Mathematics, general;
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：2198-2759

文摘

The study of the problem of simultaneous approximation by the Szász–Mirakjan–Durrmeyer type operators is carried out. An upper bound for the approximation to the rth-derivative of a function by these operators is established. Keywords Durrmeyer operators Szász–Mirakjan operators Simultaneous approximation Modulus of continuity