Uniform Approximation of Functions Belonging to $$L[0,\infty )$$-Space Using $$C^{\gamma }.T$$-Means of Fourier–Laguerre Series

Abstract

AbstractRecently, Singh and Saini [Uniform approximation in \(L [0,\infty )\)-space by Ces\(\grave{a}\)ro means of Fourier–Laguerre series. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (2021)] determined the degree of approximation of functions f belonging to \(L[0,\infty )\) by Ces\(\grave{a}\)ro means of its Fourier–Laguerre series for any \(x>0\). In this paper, we obtain the error of approximation of functions \(f\in L[0,\infty )\) using product mean \(C^{\gamma }.T (\gamma \ge 1)\) of its Fourier–Laguerre series for any \(x>0\). Further, we also discuss some particular cases of \(C^{\gamma }.T\)-means.Keywords\(C^{\gamma }.T\)-meanError of approximationFourier–Laguerre series