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Szász-Mirakjan type operators providing a better error estimation. (English) Zbl 1182.41022
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.

MSC:
41A36Approximation by positive operators