Approximations of Periodic Functions by Analogue of Zigmund's Sums in the Spaces $L^{p(\cdot)}$

TL;DR

This paper establishes order estimates for the approximation errors of Zigmund's sums in variable exponent Lebesgue spaces, advancing understanding of approximation in these flexible function spaces.

Contribution

It provides new order estimates for Zigmund's sums approximations within variable exponent Lebesgue spaces, extending classical approximation theory.

Findings

Derived upper bounds for deviations of Zigmund's sums

Applied results to classes of $(eta)$-differentiable functions

Enhanced understanding of approximation in $L^{p(ullet)}$ spaces

Abstract

In this work we found order estimates for the upper bounds of the deviations of analogue of Zigmund's sums on the classes of $(\psi;\beta)$-differentiable functions in the metrics of generalized Lebesgue spaces with variable exponent.