Asymptotic expansions for Favard operators and their left quasi-interpolants
نویسنده
چکیده
In 1944 Favard [5, pp. 229, 239] introduced a discretely defined operator which is a discrete analogue of the familiar GaussWeierstrass singular convolution integral. In the present paper we consider a slight generalization Fn,σn of the Favard operator and its Durrmeyer variant F̃n,σn and study the local rate of convergence when applied to locally smooth functions. The main result consists of the complete asymptotic expansions for the sequences (Fn,σnf) (x) and ( F̃n,σnf ) (x) as n tends to infinity. Furthermore, these asymptotic expansions are valid also with respect to simultaneous approximation. Finally, we define left quasi-interpolants for the Favard operator and its Durrmeyer variant in the sense of Sablonniere. Mathematics Subject Classification (2010): 41A36, 41A60, 41A28.
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