On Divergence of Fourier Series by Some Methods of Summability

الملخص EN

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 Bočkarev’s well-known theorems on divergence of Fourier trigonometric, Walsh, and orthonormal series is established.