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Generalized inequalities for ratio functions of trigonometric and hyperbolic functions

Marko Kostić, Yogesh J. Bagul, Christophe Chesneau

Abstract

The main aim of this note, which can be viewed as a certain addendum to the paper \cite{2019}, is to propose several generalized inequalities for the ratio functions of trigonometric and hyperbolic functions. We basically follow the approach obeyed in this paper.

Generalized inequalities for ratio functions of trigonometric and hyperbolic functions

Abstract

The main aim of this note, which can be viewed as a certain addendum to the paper \cite{2019}, is to propose several generalized inequalities for the ratio functions of trigonometric and hyperbolic functions. We basically follow the approach obeyed in this paper.

Paper Structure

This paper contains 2 sections, 5 theorems, 21 equations.

Key Result

Lemma 2.1

Suppose $u,\ v\in (0,1)$ and $k_{0}\in \{-1,0\} \cup {\mathbb N}.$ Then we have

Theorems & Definitions (12)

  • Lemma 2.1
  • proof
  • Remark 2.2
  • Proposition 2.3
  • proof
  • Proposition 2.4
  • proof
  • Proposition 2.5
  • proof
  • Remark 2.6
  • ...and 2 more