Uniform Boundedness of Kantorovich Operators in Variable Exponent Lebesgue Spaces

Abstract

    In this paper, the Kantorovich operators K_{n}, n∈ℕ are shown to be uniformly bounded in variable exponen Lebesgue spaces on the closed interval [0,1]. Also an upper estimate is obtained for the difference K_{n}(f)-f for functions f of regularity of order 1 and 2 measured in variable exponent Lebesgue spaces, which is of interest on its own and can be applied to other problems related to the Kantorovich operators.