Strong converse inequalities for Baskakov operators

On converse approximation theorems

“…This result was extended by Totik [11] to a large family of operators. Recently, Guo and Qi [7] have established a strong converse inequality of type B in terms of a unified K-functional for Baskakov operators.…”

“…[7] or [8]): let C B [0, ∞) be the set of all bounded and continuous functions on [0, ∞). For the given weight functions ϕ, φ : [0, ∞) → R and 0 < α < 2 we write…”

Direct and strong converse theorems for a general sequence of positive linear operators

“…We remark that converse results for operators L n,1 and/or S n,0 were given in [1], [4], [5], [7], [8] and [9]. For L n,a , with a > 1, the only converse inequality that we know was obtained in [13], where Theorem 2 of this paper was proved for the case λ = 0.…”

“…Theorems 1 and 2 can be used to characterize generalized Lipschitz classes as in [7], [8] and [9]. The main idea follows from the characterization of the K-functional in terms of a modulus of smoothness given in [5].…”

“…Totik [15] proved that the estimate (1) holds for a large family of operators. Guo and Qi [9] gave a strong converse inequality using a K-functional for Baskakov operators. Finta [7] extended the result of Guo and Qi to a family of linear positive operators.…”