Published online by Cambridge University Press: 20 November 2018
S. M. Nikolski [4, Theorem 1; cf. 3, esp. pp. 144 and 148] considered the remainder term in the approximation by the n-th Fejér mean, σn(x), to a function, f(x), of period 2π satisfying a Lipschitz condition of order α, 0<α≤1. In this connection, he introduced the quantity
1
where the maximum is taken over all x and the supremum is taken over all functions of period 2π, bounded by 1 (a notational convenience only) and satisfying a Laps chitz condition of order α.