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In generalized Lebesgue spaces L^{p(.)} with variable exponent p(.) definedon the real axis, we obtain several inequalities of approximation by integralfunctions of finite degree. Approximation properties of Bernstein singularintegrals in these spaces are obtained. Estimates of simultaneous approximationby integral functions of finite degree in L^{p(.)} are proved.

Approximation properties of Bernstein singular integrals in variable exponent Lebesgue spaces on the real axis