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Zbl 1182.41022
Duman, Oktay; Özarslan, M.Ali
Szász-Mirakjan type operators providing a better error estimation. (English)
[J] Appl. Math. Lett. 20, No. 12, 1184-1188 (2007). ISSN 0893-9659

Modifying the coefficients of the classical Szasz-Mirakjan operators a new class of Szasz-Mirakjan type operators is obtained. Their convergence property is proved using the Korovkin type approximation theorem. Next, using a Shisha-Mond type theorem,the approximation order of the new operators is established in terms of modulus of continuity. It is proved that this order is better as the approximation order of the classical operators. Finally, a Voronovskaja type theorem for the generalized Szasz-Mirakjan type operators is proved.
[Dan Bārbosu (Baia Mare)]

MSC 2000:: *41A36 Approximation by positive operators

Keywords: Korovkin type approximation theorem; modulus of continuity; Voronovskaja type theorem

Cited in: Zbl 1229.41015 Zbl 1181.41029

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