New bounds of Wilker- and Huygens-type inequalities for inverse trigonometric functions
type: Item
instance of: scholarly article
title: New bounds of Wilker- and Huygens-type inequalities for inverse trigonometric functions
zbMATH Open document ID: 1473.26014
author: Xiao-Diao Chen
author: Hui Wang
author: Kang Yang
author: Jin Xie
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2021-05-31T00:00:00Z
review text: In this paper, the authors use two-parameter functions to derive and prove a family of new Wilker and Huygens type inequalities involving inverse trigonometric functions. The results obtained yield in most cases previous results of these type in the literature and also show a much better approximation performance than those of prevailing methods. Numerical examples are given to demonstrate that this new method yields better approximation than the previous methods.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 26D05
Mathematics Subject Classification ID: 26D07
zbMATH DE Number: 7352844
zbMATH Keywords: Wilker- and Huygens-type inequality
zbMATH Keywords: tighter bounds
zbMATH Keywords: integral approximation error
zbMATH Keywords: inverse trigonometric function
zbMATH Keywords: two-parameter function
MaRDI profile type: Publication
full work available at URL: s13398-020-00969-2
OpenAlex ID: W3118641581
cites work: Some notes on a method for proving inequalities by computer
cites work: Series representations of the remainders in the expansions for certain trigonometric functions and some related inequalities, I
cites work: Sharp Wilker- and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions
cites work: Inequality chains for Wilker, Huygens and Lazarević type inequalities
cites work: Inequalities related to certain inverse trigonometric and inverse hyperbolic functions
cites work: On the Wilker and Huygens-type inequalities
cites work: A new method for sharpening the bounds of several special functions
cites work: A new method for refining the Shafer's equality and bounding the definite integrals
cites work: A two-point-Padé-approximant-based method for bounding some trigonometric functions
cites work: Generalized Wilker-type inequalities with two parameters
cites work: Refinements of Jordan-Stečkin and Becker-Stark inequalities
cites work: The natural algorithmic approach of mixed trigonometric-polynomial problems
cites work: Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities
cites work: A method for proving some inequalities on mixed trigonometric polynomial functions
cites work: A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions
cites work: A proof of an open problem of Yusuke Nishizawa for a power-exponential function
cites work: The natural approach of Wilker-Cusa-Huygens inequalities
cites work: A subtly analysis of Wilker inequality
cites work: On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities
cites work: Wilker and Huygens-type inequalities for the generalized trigonometric and for the generalized hyperbolic functions
cites work: Some improvements of Jordan-Steckin and Becker-Stark inequalities
cites work: New approximations of some expressions involving trigonometric functions
cites work: Refined estimates and generalizations of inequalities related to the arctangent function and Shafer's inequality
cites work: Shafer-Fink type inequalities for arc lemniscate functions
cites work: A further refinement of Wilker's inequality
cites work: Several improvements of Mitrinovic-Adamovic and Lazarevics inequalities with applications to the sharpening of Wilker-type inequalities
cites work: Padé approximants for inverse trigonometric functions and their applications
cites work: Sharpened versions of Mitrinović-Adamović, Lazarević and Wilker's inequalities for trigonometric and hyperbolic functions
cites work: Sharp Cusa type inequalities with two parameters and their applications
cites work: A refinement of the Becker-Stark inequalities
cites work: New bounds for the exponential function with cotangent
cites work: New approximation inequalities for circular functions
cites work: Sharp inequalities of Mitrinovic-Adamovic type
cites work: On Frame's inequalities
cites work: An unity of Mitrinovic-Adamovic and Cusa-Huygens inequalities and the analogue for hyperbolic functions
cites work: On Wilker-type inequalities
cites work: New Mitrinović-Adamović type inequalities
cites work: Some new bounds for Sinc function by simultaneous approximation of the base and exponential functions
cites work: New inequalities of Wilker's type for circular functions
cites work: Refinements of Huygens- and Wilker-type inequalities
DOI: 10.1007/S13398-020-00969-2
description: scientific article; zbMATH DE number 7352844