Seminormed approximation of functions by operators based on their Fourier series (Q6553383)

The authors investigate the degree of approximation in $L_p$-norm using an operator based on the partial sums of a function's Fourier series. They extend previous results by weakening certain continuity and monotonicity conditions, offering improvements over findings by \textit{U.~Deǧer} and \textit{H.~Bayındır} [Azerb. J. Math. 8, No.~2, 122--141 (2018; Zbl 1418.42005)] and, additionally, \textit{U.~Singh} and \textit{S.~Sonker} [Commun. Comput. Inf. Sci. 283, 1--10 (2012; Zbl 1494.42001)]. By employing the modulus of continuity under weaker conditions, the authors enhance approximation results in function spaces beyond the restrictions seen in previous works. The paper contributes to the field by broadening the applicability of approximation methods in Fourier analysis.