Approximation by $T$ means with respect to Vilenkin system in Lebesgue spaces and Lipschitz classes

TL;DR

This paper investigates the approximation properties of $T$ means with respect to the Vilenkin system in Lebesgue and Lipschitz spaces, extending known inequalities and providing new theoretical insights.

Contribution

It introduces new results on $T$ means approximation in Lebesgue and Lipschitz spaces, expanding the theoretical framework for Vilenkin system approximations.

Findings

Extended approximation inequalities for $T$ means

New bounds in Lebesgue spaces

Improved understanding of Lipschitz class approximations

Abstract

In this paper we present and prove some new results concerning approximation properties of $T$ means with respect to the Vilenkin system in Lebesgue spaces and Lipschitz classes for any $1\leq p<\infty$. As applications, we obtain extension of some known approximation inequalities.