On Lazarevic and Cusa type inequalities for hyperbolic functions with two parameters

2014/08/10 by Zhen-Hang Yang, Yang, Zhen-Hang
Mathematics · #26D158 #33B10 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Primary 26D05 #Secondary 26A48 #math.CA #msc:26A48 #msc:26D05 #msc:26D158 #msc:33B10

paper · pdf · doi:10.48550/arxiv.1408.2248

20 pages

arxiv created 2014/08/10 · openalex publication_date 2014/08/10 · arxiv updated 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by investigating the monotonicity of a function composed of % ( \sinh x) /x and \cosh x with two parameters in x on % ( 0,∞ ) , we prove serval theorems related to inequalities for hyperbolic functions, which generalize known results and establish some new and sharp inequalities. As applications, some new and sharp inequalities for bivariate means are presented.

Related

• Trigonometric and Hyperbolic Inequalities
• Some new inequalities for trigonometric functions and corresponding ones for means
• A sharp inequality involving hyperbolic and inverse hyperbolic functions
• A note on certain inequalities for bivariate means
• On classical inequalities of trigonometric and hyperbolic functions