TY - JOUR AU - Nigam, H. K. AU - Mursaleen, Mohammad AU - Rani, Supriya PY - 2021 DA - 2021/01/07 TI - Approximation of function using generalized Zygmund class JO - Advances in Difference Equations SP - 34 VL - 2021 IS - 1 AB - In this paper we review some of the previous work done by the earlier authors (Singh et al. in J. Inequal. Appl. 2017:101, 2017; Lal and Shireen in Bull. Math. Anal. Appl. 5(4):1–13, 2013), etc., on error approximation of a function g in the generalized Zygmund space and resolve the issue of these works. We also determine the best error approximation of the functions g and $g^{\prime }$, where $g^{\prime }$is a derived function of a 2π-periodic function g, in the generalized Zygmund class $X_{z}^{(\eta )}$, $z\geq 1$, using matrix-Cesàro $(TC^{\delta })$means of its Fourier series and its derived Fourier series, respectively. Theorem 2.1 of the present paper generalizes eight earlier results, which become its particular cases. Thus, the results of (Dhakal in Int. Math. Forum 5(35):1729–1735, 2010; Dhakal in Int. J. Eng. Technol. 2(3):1–15, 2013; Nigam in Surv. Math. Appl. 5:113–122, 2010; Nigam in Commun. Appl. Anal. 14(4):607–614, 2010; Nigam and Sharma in Kyungpook Math. J. 50:545–556, 2010; Nigam and Sharma in Int. J. Pure Appl. Math. 70(6):775–784, 2011; Kushwaha and Dhakal in Nepal J. Sci. Technol. 14(2):117–122, 2013; Shrivastava et al. in IOSR J. Math. 10(1 Ver. I):39–41, 2014) become particular cases of our Theorem 2.1. Several corollaries are also deduced from our Theorem 2.1. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-020-03197-5 DO - 10.1186/s13662-020-03197-5 ID - Nigam2021 ER -