Approximation by some combinations of the Poisson integrals for Hermite and Laguerre expansions
Abstract
The aim of this paper is the study of a rate of convergence of some combinations of the Poisson integrals for Hermite and Laguerre expansions. We are able to achieve faster convergence for our modified operators over the Poisson integrals. We prove also the Voronovskaya type theorem for these new operators.
References
O. Duman, M.A. Özarslan, Szász-Mirakjan type operators providing a better error estimation, Appl. Math. Lett. 20 (2007), 1184–1188.
##plugins.generic.googleScholarLinks.settings.viewInGS##
G. Krech, On the rate of convergence theorem for the alternate Poisson integrals for Hermite and Laguerre expansions, Ann. Acad. Pedagog. Crac. Stud. Math. 4 (2004), 103–110.
##plugins.generic.googleScholarLinks.settings.viewInGS##
N.N. Lebedev, Special functions and their applications, Revised edition, Dover Publications, Inc., New York, 1972. Approximation by some combinations of the Poisson integrals [29]
##plugins.generic.googleScholarLinks.settings.viewInGS##
B. Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions, Trans. Amer. Math. Soc. 139 (1969), 231–242.
##plugins.generic.googleScholarLinks.settings.viewInGS##
M.A. Özarslan, O. Duman, Approximation properties of Poisson integrals for or- thogonal expansions, Taiwanese J. Math. 12 (2008), 1147–1163.
##plugins.generic.googleScholarLinks.settings.viewInGS##
G. Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, v. 23, American Mathematical Society, New York, 1939.
##plugins.generic.googleScholarLinks.settings.viewInGS##
G. Toczek, E. Wachnicki, On the rate of convergence and the Voronovskaya the- orem for the Poisson integrals for Hermite and Laguerre expansions, J. Approx. Theory 116 (2002), 113–125.
##plugins.generic.googleScholarLinks.settings.viewInGS##
D.K. Verma, V. Gupta, P.N. Agrawal, Some approximation properties of Baskakov-Durrmeyer-Stancu operators, Appl. Math. Comput. 218 (2012), 6549– 6556.
##plugins.generic.googleScholarLinks.settings.viewInGS##
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