Abstract
In the present paper, we study some theorems on approximation of the r-th derivative of a given function f by corresponding r-th derivative of the generalized Bernstein operator.
Similar content being viewed by others
References
Deo N.: A note on equivalence theorem for Beta operators. Mediterr. J. Math. 4(2), 245–250 (2007)
Deo N.: Direct result on exponential-type operators. Appl. Math. Comput. 204, 109–115 (2008)
Deo N.: Direct result on the Durrmeyer variant of Beta operators. Southeast Asian Bull. Math. 32, 283–290 (2008)
Deo N., Noor M.A., Siddiqui M.A.: On approximation by a class of new Bernstein type operators. Appl. Math. Comput. 201, 604–612 (2008)
Derriennic M.M.: Surl’approximation des fonctions integrables sur [0, 1] par des polynomes de Bernstein modifies. J. Approx. Theory 31, 325–343 (1981)
Durrmeyer, J.L.: Une formule d’inversion de la transformée de Laplace-applications à la théorie des moments, Thése de 3e cycle, Faculté des Sciences de l’ Université de Paris (1967)
Gupta V.: A note on modified Bernstein polynomials. Pure Appl. Math. Sci. 44(1–2), 604–612 (1996)
Gupta V., Srivastava G.S.: Approximation by Durrmeyer type operators. Ann. Polon. Math. LXIV 2, 153–159 (1996)
Heilmann M.: Direct and converse results for operators of Baskakov–Durrmeyer type. Approx. Theory Appl. 5(1), 105–127 (1989)
Singh S.P., Varshney O.P.: A note on convergence of linear positive operators. J. Approx. Theory 39, 51–55 (1983)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Deo, N., Bhardwaj, N. & Singh, S.P. Simultaneous approximation on generalized Bernstein–Durrmeyer operators. Afr. Mat. 24, 77–82 (2013). https://doi.org/10.1007/s13370-011-0041-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13370-011-0041-y