On the Favard-Type Theorem and the Jackson-Type Theorem (II)

Let R = ( − ∞ , ∞ ) , and let 𝑄 ∈ ℂ 1 ∶ ℝ → [ 0 , ∞ ) be an even function. We consider the exponential weights 𝑤 ( 𝑥 ) = 𝑒 − 𝑄 ( 𝑥 ) , 𝑥 ∈ ℝ . In this paper we investigate the relations between the Favard-type inequality and the Jackson-type inequality. We also discuss the equivalence of two K-functionals and the modulus of smoothness.