On Divergence of Fourier Series by Some Methods of Summability

A new summability method of series is introduced and studied. The particular cases of this method are, for example, variable-order Cesaro and Riesz methods. Applications to divergence problem of Fourier series are given. An extension of Kolmogorov, Schipp, and Bo？karev’s well-known theorems on divergence of Fourier trigonometric, Walsh, and orthonormal series is established.