On classical inequalities of trigonometric and hyperbolic functions

TL;DR

This collection of research papers refines and establishes new inequalities for trigonometric and hyperbolic functions, explores their interrelations, and derives bounds for the beta function, advancing mathematical inequality theory.

Contribution

The papers provide improved bounds and relations for classical inequalities involving trigonometric, hyperbolic functions, and the beta function, with new sharp bounds and connections.

Findings

Refined Adamovic-Mitrinovic and Cusa-Huygens inequalities

Established sharp bounds for the beta function

Built relations between trigonometric and hyperbolic functions

Abstract

This article is the collection of the six research papers, recently written by the authors. In these papers authors refine the inequalities of trigonometric and hyperbolic functions such as Adamovic-Mitrinovic inequality, Cusa-Huygens inequality, Lazarevic inequality, Huygens inequality, Jordan's inequality, Carlson's inequality, Wilker's inequality, Redheffer's inequality, Wilker-Anglesio inequality, Becker-Stark inequality, Kober's inequality, Shafer's inequality and Shafer-Fink's inequality. The relation between trigonometric and hyperbolic functions has been built too. In the last paper, the sharp upper and lower bounds for the classical beta function has been established by studying the Jordan's inequality.