Starting from a general sequence of linear and positive operators of discrete type, we associate its r-th order generalization. This construction involves high order derivatives of a signal and it looses the positivity property. Considering that the initial approximation process is A-statistically uniform convergent, we prove that the property is inherited by the new sequence. Also, our result includes information about the uniform convergence. Two applications in q-Calculus are presented. We study q-analogues both of Meyer-König and Zeller operators and Stancu operators.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
positive approximation process; A-statistical uniform convergence; matrix summability method
O. Agratini, Statistical convergence of a non-positive approximation process, Chaos, Solitons & Fractals, 44 (2011) no. 11, pp. 977-981, https://doi.org/10.1016/j.chaos.2011.08.003
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Chaos, Solitons & Fractals
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