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Equi-statistical convergence of positive linear operators. (English) Zbl 1131.41008
The authors study a Korovkin-type approximation theorem using the equi-statistical convergence which is stronger than the statistical uniform convergence. By an example it is shown that the new approximation result works while its classical and statistical cases do not work. Furthermore, the rate of equi-statistical convergence of a sequence of positive linear operators is computed, and a Voronovskaya-type theorem in the equi-statistical sense for a sequence of positive linear operators constructed by means of the Bernstein polynomials is given.
MSC:
41A36Approximation by positive operators
40A30Convergence and divergence of series and sequences of functions
41A30Approximation by other special function classes
41A25Rate of convergence, degree of approximation
References:
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