Resumen de Modulus of Smoothness and Theorems Concerning Approximation in the Space L2q,α(Rq) with Power Weight

Radouan Daher, Othman Tyr

• In this work, we look at problems in the theory of approximation of functions on the space L2q,α(Rq) with power weight. We prove analogues of the direct Jackson’s theorems for the modulus of smoothness (of arbitrary order) constructed using the generalized q-Dunkl translation operator. We also show that the modulus of smoothness and the K-functional constructed from the Sobolev-type space corresponding to the q-Dunkl operator are equivalent.