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Statistical convergence of a non-positive approximation process

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  • Agratini, Octavian

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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  • Agratini, Octavian, 2011. "Statistical convergence of a non-positive approximation process," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 977-981.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:11:p:977-981
    DOI: 10.1016/j.chaos.2011.08.003
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    References listed on IDEAS

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    1. Ali Özarslan, M. & Duman, Oktay, 2009. "Approximation theorems by Meyer-König and Zeller type operators," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 451-456.
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