On the degree of approximation by Gauss Weierstrass integrals (Q1578347)

\textit{Y. Hasegawa} [Kōdai Math. Semin. Rep. 15, 226-238 (1963; Zbl 0127.29302)] proved a result to obtain the degree of approximation of a certain class of functions by means of the first arithmetic means of double Fourier series of an appropriately Lebesgue integrable function \(f\) of two variables. In the present paper the authors determine the degree of approximation for the functions belonging to a certain class of functions by means of the Gauss--Weierstrass integral of the double Fourier series of \(f\) .