Abstract
In this paper, the Kantorovich operators Kn, n ? N are shown to be uniformly bounded in variable exponent Lebesgue spaces on the closed interval [0; 1]. Also an upper estimate is obtained for the difference Kn(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.
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