Modified Kantorovich Operators Providing a Better Error Estimation

Abstract

Abstract:The approximation operator for every kind of the objective function is different in approximation theory. For Lebesgue function, we introduce a kind of modified Kantorovich operators, which preserve the test functions 1 and 2x . This type of modification enables better error estimation on the interval 3 3 [ ) , +∞ than the classic ones. Finally, a Voronovskaya-type theorem for these operators is also obtained.