Slight extensions of some theorems on the rate of pointwise approximation of functions from some subclasses of <i>L^p</i>

Abstract

Abstract. In this paper we prove some results on the rate of pointwise approximation of functions by means of some matrix transformations related to the partial sums of a Fourier series, removing the assumptions that entries of the considered matrix belong to the classes RBV S or HBV S. In fact, with weaker assumptions, our results give better degrees than those obtained previously. Moreover, some results that have been obtained earlier follow from our results as special cases. Finally, we present some theorems of such type involving the so-called γRBV S or γHBV S classes of numerical sequences.

Pointwise approximation of modified conjugate functions by matrix operators of conjugate Fourier series of 2 π / r $2\pi /r$ -periodic functions

“…Considering the above remarks and the obvious inequality our results also improve and generalize the mentioned result of Krasniqi [ 1 ].…”

“…Taking the conditions ( 11 ) and ( 13 ) in Theorem 1 reduce to ( 1 ) and ( 2 ). Thus we obtain the results from [ 2 ] and Theorem A [ 1 , Theorem 8, p . 95], but in the case of [ 3 ] ( Theorem B and C ) we reduce the assumptions .…”

Degrees of the approximation of integrable functions by some special matrix means of fourier series

“…Some generalization of this deviation for the sequence (a n,k ) n k=0 belonging to class HBVS, or RBVS respectively, is also in Krasniqi's paper [2].…”