On the Favard-type theorem and the Jackson-type theorem. II (Q420253)

Summary: Let \(R = (-\infty, \infty)\), and let \(Q \in \mathbb C^1 : \mathbb R \rightarrow [0, \infty)\) be an even function. We consider the exponential weights \(w(x) = e^{-Q(x)}, ~x \in \mathbb R\). 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. For part I, cf. [\textit{R. Sakai} and \textit{N. Suzuki}, J. Res. Inst. Meijo University, No. 10, 29--33 (2011)].