Inequalities similar to those of Bernstein for non-periodic splines in $L_2$ space

TL;DR

This paper establishes Bernstein-like inequalities for non-periodic splines within the $L_2$ space, extending classical approximation theory results to a broader class of functions.

Contribution

It introduces new Bernstein-type inequalities for non-periodic splines in $L_2$, expanding the theoretical framework of spline approximation.

Findings

Proved Bernstein-like inequalities for non-periodic splines in $L_2$

Extended classical inequalities to a broader spline class

Provided theoretical bounds for spline approximation in $L_2$

Abstract

We prove Inequalities similar to those of Bernstein for non-periodic splines in $L_2$ space.