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Bleimann, Butzer, and Hahn Operators Based on the q-Integers
(Hindawi Publishing Corporation, 2007) Aral, Ali; Dogru, Oguen
We give a new generalization of Bleimann, Butzer, and Hahn operators, which includes q-integers. We investigate uniform approximation of these new operators on some subspace of bounded and continuous functions. In Section 3, we show that the rates of convergence of the new operators in uniform norm are better than the classical ones. We also obtain a pointwise estimation in a general Lipschitz-type maximal function space. Finally, we de? fine a generalization of these new operators and study the uniform convergence of them. Copyright (C) 2007.
On Kantorovich process of a sequence of the generalized linear positive operators
(Taylor & Francis Inc, 2008) Ispir, Nurhayat; Aral, Ali; Dogru, Oguen
We define the Kantorovich variant of the generalized linear positive operators introduced by Ibragimov and Gadjiev in 1970. We investigate direct approximation result for these operators on p-weighted integrable function spaces and also estimate their rate of convergence for absolutely continuous functions having a derivative coinciding a.e., with a function of bounded variation.