Uniform Boundedness of Kantorovich Operators in Variable Exponent Lebesgue Spaces

Rabil AYAZOGLU(Mashiyev), Sezgin Akbulut, Ebubekir Akkoyunlu

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.


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