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 exponent 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.

The Existence and Uniqueness of an Entropy Solution to Unilateral Orlicz Anisotropic Equations in an Unbounded Domain

“…For more results we refer the reader to the work [16]. We mention [17][18][19], for the Sobolev space with variable exponent, and [20][21][22][23][24][25][26] for the classical anisotropic space. The oddity of our present paper is to continue in this direction and to show the existence and uniqueness of entropy solution for equations (P ) governed with growth and described by an N-uplet of N-functions satisfying the ∆ 2 -condition, within the fulfilling of anisotropic Orlicz spaces.…”