Generalized Bernstein Kantorovich operators: Voronovskaya type results, convergence in variation

Acu, Ana Maria, Aral, Ali and Raşa, Ioan

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This paper includes Voronovskaya type results and convergence in variation for the exponential Bernstein Kantorovich operators. The Voronovskaya type result is accompanied by a relation between the
mentioned operators and suitable auxiliary discrete operators. Convergence of the operators with respect to the variation seminorm is obtained in the space of functions with bounded variation. We propose a general framework covering the results provided by previous literature.



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Aral, Ali, Acu, Ana Maria, Raşa, Ioan