Considering a general class of discrete linear positive operators, by using a one-to-one function, we associate to the class mentioned above a new sequence of operators. Our aim is to establish the transfer of approximation properties on this construction. The study is carried out in a weighted space and our results are materialized in obtaining both a convergence the Theorem of Korovkin type and an inequality for the approximation error expressed in terms of a certain weighted modulus of smoothness. Two particular cases are analyzed.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Approximation process; Markov type operator; Weighted space; Weighted approximation; Modulus of smoothness.
O. Agratini, A sequence of positive linear operators associated with an approximation process, Applied Mathematics and Computation, 269 (2015), pp. 23-28. https://doi.org/10.1016/j.amc.2015.07.043
(requires subscription) https://doi.org/10.1016/j.amc.2015.07.043
Applied Mathematics and Computation
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