A Bernstein type inequality for the Askey-Wilson operator

Abstract We establish a Riesz-type interpolation formula on the interval [ − 1 , 1 ] for the Askey–Wilson operator. As consequences, sharp Bernstein inequality and Markov inequality are obtained when differentiation is replaced by the Askey–Wilson operator. Moreover, an inverse approximation theorem is proved using a Bernstein type inequality in L 2 -space. We conclude our paper with an overconvergence result which is applied to characterize all q -differentiable functions of Brown and Ismail.