Strong Converse Inequalities and Quantitative Voronovskaya-Type Theorems for Trigonometric Fejér Sums

Abstract

Let σn denotes the classical Fejér operator for trigonometric expansions. For a fixed even integer r, wecharacterize the rate of convergence of the iterative operators (I − σn)r(f) in terms of the modulus of continuity oforder r (with specific constants) in all Lp spaces 1 ≤ p ≤ ∞. In particular, the constants depend not on p. Moreover,we present a quantitative version of the Voronovskaya-type theorems for the operators (I − σn)r(f).