Geodesic
On Global Inverse Theorems of Szász and Baskakov Operators
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 255-263

Voir la notice de l'article provenant de la source Cambridge University Press

The Szász and Baskakov approximation operators are given by 1.1 1.2 respectively. For continuous functions on [0, ∞) with exponential growth (i.e. ‖ƒ‖A ≡ supx \ƒ(x)e–Ax\ < M) the modulus of continuity is defined by 1.3 where ƒ ∈ Lip* (∝, A) for some 0 < ∝ ≦ 2 if w 2(ƒ, δ, A) ≦ Mδ∝ for all δ < 1. We shall find a necessary and sufficient condition on the rate of convergence of An(ƒ, x) (representing Sn(ƒ, x) or Vn (ƒ, x)) to ƒ(x) for ƒ(x) ∈ Lip* (∝, A). In a recent paper of M. Becker [1] such conditions were found for functions of polynomial growth (where (1 + \x\N )−1 replaced e–Ax in the above). M. Becker explained the difficulties in treating functions of exponential growth. 
Ditzian, Z. On Global Inverse Theorems of Szász and Baskakov Operators. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 255-263. doi: 10.4153/CJM-1979-027-2
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