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Generalized Bernstein Kantorovich operators: Voronovskaya type results, convergence in variation
(North Univ Baia Mare, 2022) Acu, Ana Maria; Aral, Ali; Rasa, Ioan
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.
On the Modification of Mellin Convolution Operator and Its Associated Information Potential
(Taylor & Francis Inc, 2023) Ozsarac, Firat; Acu, Ana Maria; Aral, Ali; Rasa, Ioan
In this paper, we define a new generalization of Mellin-Gauss-Weierstrass operators that preserve logarithmic functions. We compute logarithmic moments of the new operators and describe the behavior of the modified operators in some weighted spaces. The weighted approximation properties of operators including weighted approximation and weighted quantitative type approximation properties, using weighted logarithmic modulus of continuity, are presented. Using the Mellin-Gauss-Weierstrass kernel p(., .) as a logarithmic probability density, we study the associated information potential, the expected value E[log p(., .)] and the variance Var[log p(., .)].