Some Remarks on the Best Approximation Rate of Certain Trigonometric   Series
  The main object of the present paper is to give a complete result regarding the best approximation rate of certain trigonometric series in general complex valued continuous function space under a new condition which gives an essential generalization to $O$-regularly varying quasimonotonicity. An application is present in Section 3. 
Song-Ping Zhou and Rui-Jun Le