A strong converse estimate of the rate of approximation by the Kantorovich operator in variable exponent Lebesgue spaces
摘要
We establish a strong converse inequality by a K-functional of the rate of approximation by the Kantorovich operators in variable exponent Lebesgue spaces. It shows that a recently obtained direct inequality is optimal. A Voronovskaya inequality is also proved. The approach applied heavily relies on the boundedness of the Hardy-Littlewood maximal operator.