Statistical convergence of a non-positive approximation process |
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Authors: | Octavian Agratini |
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Institution: | Babe?-Bolyai University, Faculty of Mathematics and Computer Science, Kog?lniceanu 1, 400084 Cluj-Napoca, Romania |
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Abstract: | 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. |
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