Best approximations of periodic functions in generalized lebesgue spaces - Chaichenko, S. O. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
In generalized Lebesgue spaces with variable exponent, we determine the order of the best approximation on the classes of (ψ, β)-differentiable 2π-periodic functions. We also obtain an analog of the well-known Bernstein inequality for the (ψ, β)-derivative, with the help of which the converse theorems of approximation theory are proved on the indicated classes.