Approximation problems in the Lebesgue spaces with variable exponent

In the variable exponent Lebesgue space, the r-th modulus of smoothness (r = 1,2, ... ) is defined and in this term, the direct and inverse theorems of approximation theory are proved. Moreover, the constructive characterization problems for the some subclasses are discussed. (C) 2017 Elsevier Inc. All rights reserved.