Order of Approximation by a New Univariate Kantorovich Type Operator

Abstract

In order to approximate Lebesgue integrable functions on [0, 1], a sequence of linear positive integral operators of Kantorovich type Lσ<sσ>f (x) with a parameter sσ is introduced. The estimates for rates of approximation for functions with a specific smoothness are proved using the appropriate modulus of continuity.