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.
"A-Statistical Convergence of a Class of Integral operators,"
Applied Mathematics & Information Sciences: Vol. 06
, Article 20.
Available at: https://dc.naturalspublishing.com/amis/vol06/iss2/20