A-statistical convergence of a class of integral operators


Starting from a general sequence of linear and positive operators of summation integral 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 pointwise convergent, we prove that the property is inherited by the new sequence. The study is developed for smooth functions defined both on an unbounded interval and on a compact interval.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Positive linear operator, statistical convergence, approximation process.

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O. Agratini, A-statistical convergence of a class of integral operators, Nonlinear Analysis: Theory, Methods & Applications, 75 (2012) no. 8, pp. 3465-3469. 


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Applied Mathematics & Information Sciences

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