Strong Converse Inequalities and Qantitative Voronovskaya-Type Theorems for Trigonometric Fej\'er Sums

Year 2020, , 53 - 63, 01.06.2020

Jorge Bustamante , Lázaro Flores De Jesús

https://doi.org/10.33205/cma.653843

Cited By: 7

Abstract

Let $\sigma_n$ denotes the classical Fej\'er operator for trigonometric expansions.
For a fixed even integer $r$, we characterize the rate of convergence of the iterative operators
$(I-\sigma_n)^r(f)$ in terms of the modulus of continuity of order $r$ (with specific constants)
in all $\mathbb{L}^p$ spaces $1\leq p \leq \infty$. In particular, the constants depend not on $p$.
Moreover, we present a quantitative version of the Voronovskaya-type theorems for the operators
$(I-\sigma_n)^r(f)$.

Keywords

Fej\'er operators, iterative combinations, rate of convergence, direct and converse results

Supporting Institution

Benemerita Universidad Autonnoma de Puebla

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