Approximation in Smirnov classes with variable exponent
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In this work, the inverse problem of approximation theory in the variable exponent Smirnov classes of analytic functions, defined on the Jordan domains with a Dini-smooth boundaries, is studied. First, for this purpose, an inverse theorem in the variable exponent Lebesgue spaces of 2 pi periodic functions is obtained. Later, using the special linear operators, this inverse theorem to the variable exponent Smirnov classes of analytic functions is moved.