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Abel transforms of positive linear operators on weighted spaces. (English) Zbl 1308.41020
Summary: The classical Korovkin approximation theory deals with the convergence of a sequence of positive linear operators. When the sequence of positive linear operators does not converge it will be useful to use some summability methods. In this paper we use the Abel method, a sequence-to-function transformation, to study a Korovkin type approximation theorem for positive linear operators acting from a weighted space \(C_{\rho_{1}}\) into a weighted space \(B_{\rho_{2}}.\) Moreover using the modulus of continuity we also give rate of Abel convergence.

MSC:
41A25 Rate of convergence, degree of approximation
41A36 Approximation by positive operators
40A05 Convergence and divergence of series and sequences
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Full Text: Euclid