Approximation of classes of functions defined by a generalized $r$-th   modulus of smoothness
  In this paper, a $k$-th generalized modulus of smoothness is defined based on an asymmetric operator of generalized translation and a theorem is proved about the coincidence of class of functions defined by this modulus and a class of functions having given order of best approximation by algebraic polynomials. 
Mikhail K. Potapov and Faton M. Berisha
math.FA