On certain new means generated by generalized trigonometric functions

TL;DR

This paper introduces new generalized means derived from generalized trigonometric functions and establishes inequalities involving these means, expanding the mathematical understanding of mean relationships.

Contribution

The paper generalizes classical means using generalized trigonometric functions and derives new inequalities, offering novel insights into mean relationships.

Findings

Introduction of new generalized means from generalized trigonometric functions

Establishment of several two-sided inequalities involving these means

Extension of classical mean inequalities to new generalized forms

Abstract

In this paper, authors generalize logarithmic mean $L$, Neuman-S\'andor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these generalized means are established.