Remarks on Redheffer's inequality

TL;DR

This paper explores Redheffer's inequality and its extensions to analyze the first eigenvalue of the p-Laplacian and generalize inequalities for trigonometric functions, providing new bounds and insights.

Contribution

It extends Redheffer's inequality to broader classes and applies it to estimate the first eigenvalue of the p-Laplacian.

Findings

Derived bounds for the first eigenvalue of p-Laplacian.

Extended Redheffer-type inequality to generalized trigonometric functions.

Provided new estimates for mathematical functions using Redheffer's inequality.

Abstract

Redheffer's inequality and its extensions are applied to study the behavior and estimates of the first eigenvalue of $p$-Laplacian with respect to $p$. Furthermore, a Redheffer-type inequality for the generalized trigonometric function is extended to a broader class.