Inequalities for eigenfunctions of the $p$-Laplacian

TL;DR

This paper investigates inequalities related to eigenfunctions of the one-dimensional p-Laplace operator, extending classical trigonometric and hyperbolic function inequalities to their p-analogues.

Contribution

It introduces new inequalities for p-analogues of trigonometric and hyperbolic functions and their inverses, expanding the understanding of eigenfunctions of the p-Laplacian.

Findings

Established inequalities for p-sine functions and their inverses.

Derived inequalities for p-hyperbolic functions and their inverses.

Extended classical inequalities to the p-analogue setting.

Abstract

Motivated by the work of P. Lindqvist, we study eigenfunctions of the one-dimensional $p$-Laplace operator, the $\sin_p$ functions, and prove several inequalities for these and $p$-analogues of other trigonometric functions and their inverse functions. Similar inequalities are given also for the $p$-analogues of the hyperbolic functions and their inverses.