Bernstein-nikolskii-stechkin inequality and Jackson’s theorem for the index Whittaker transform

Abstract

In this paper, by using the Whittaker translation operators studied recently by Sousa et al., we define the modulus of smoothness associated with the index Whittaker operator. Moreover, we prove Bernstein-Nikolskii-Stechkin inequality for the index Whittaker transform. As an application, we establish an equivalence theorem between K-functionals and a modulus of smoothness in \(L^{2}(\mu _{\alpha })\). We conclude this paper by studying Jackson’s theorem associated with the index Whittaker transform.