On the Approximation Properties of Cesàro Means of Negative Order of Walsh–Fourier Series Original Research Article

In this paper we establish approximation properties of Cesàro (C, −α)-means with α∈(0, 1) of Walsh–Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ−αn(f, x) to f(x) in the Lp -metric. We also show that this condition cannot be improved in the case p=1.