(1) Faculty of Physics and Mathematics, Sukhumi Branch of I. Javakhishvili Tbilisi State University, 1, I. Chavchavadze ave., Tbilisi, 380028, Georgia
Abstract:
The necessary and sufficient conditions of the absolute convergence of a trigonometric Fourier series are established for continuous 2-periodic functions which in [0, 2] have a finite number of intervals of convexity, and whose nth Fourier coefficients are O((l/n; f)/n), where ( f) is the continuity modulus of the function f.