Strong Converse Inequality for Weighted Approximation of Functions by the Szász–Mirakjan–Kantorovich Operator

We investigate the weighted approximation of functions in \(L_p\) $L_p$ -norm by Kantorovich modifications of the classical Szász-Mirakjan operator, with weights of type \((1+x)^{\alpha }\) ${(1+x)}^{\alpha }$ , \(\alpha \in {\mathbb {R}}\) $\alpha \in \mathbb{R}$ . By using an appropriate K-functional we prove a strong converse inequality for the weighted error of approximation and characterize it exactly. We prove a Voronovskaya and Bernstein-type inequalities for the Szász-Mirakjan–Kantorovich operator.