Application of the even-type delayed mean in the approximation of functions from the generalized Zygmund class with weight

UDC 517.5 We introduce a new class of functions, namely, the generalized Zygmund class with weight. Moreover, we determine the degree of approximation for functions belonging to this class. The degree of approximation is expressed in terms of two moduli of continuity of the second order $w_1$ and $w_2$ such that $w_1/w_2$ is positive and nondecreasing. To realize this task, for approximation we use the even-type delayed mean of their Fourier series.