Statistical convergence of a non-positive approximation process

Octavian Agratini

Chaos, Solitons & Fractals, 2011, vol. 44, issue 11, 977-981

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:11:p:977-981

DOI: 10.1016/j.chaos.2011.08.003

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