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Keywords = wilker-type inequality

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23 pages, 5446 KiB  
Article
A Parametric Method for Proving Some Analytic Inequalities
by Branko Malešević, Miloš Mićović and Bojana Mihailović
Axioms 2024, 13(8), 520; https://doi.org/10.3390/axioms13080520 - 1 Aug 2024
Cited by 3 | Viewed by 1195
Abstract
In this paper, a parametric method for proving inequalities is described. The method is based on associating a considered inequality with the corresponding stratified family of functions. Many inequalities from the theory of analytic inequalities can be interpreted using families of functions that [...] Read more.
In this paper, a parametric method for proving inequalities is described. The method is based on associating a considered inequality with the corresponding stratified family of functions. Many inequalities from the theory of analytic inequalities can be interpreted using families of functions that are stratified with respect to some parameter. By discussing the sign of the functions from the family by the parameter according to which the family is stratified, inequalities are obtained that contain the best possible constants, if they exist. The application of this method is demonstrated for four inequalities: the Cusa–Huygens inequality, the Wilker-type inequality and the two Mitrinović–Adamović-type inequalities. Significantly simpler proofs and improvements of all these inequalities are provided. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities II)
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13 pages, 254 KiB  
Article
Refinements of Wilker–Huygens-Type Inequalities via Trigonometric Series
by Gabriel Bercu
Symmetry 2021, 13(8), 1323; https://doi.org/10.3390/sym13081323 - 22 Jul 2021
Cited by 2 | Viewed by 1638
Abstract
The study of even functions is important from the symmetry theory point of view because their graphs are symmetrical to the Oy axis; therefore, it is essential to analyse the properties of even functions for x greater than 0. Since the functions [...] Read more.
The study of even functions is important from the symmetry theory point of view because their graphs are symmetrical to the Oy axis; therefore, it is essential to analyse the properties of even functions for x greater than 0. Since the functions involved in Wilker–Huygens-type inequalities are even, in our approach, we use cosine polynomials expansion method in order to provide new refinements of the above-mentioned inequalities. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)
24 pages, 291 KiB  
Article
High Precision Wilker-Type Inequality of Fractional Powers
by Ling Zhu
Mathematics 2021, 9(13), 1476; https://doi.org/10.3390/math9131476 - 24 Jun 2021
Cited by 1 | Viewed by 1971
Abstract
This paper established a new high precision Wilker-type inequality with fractional powers for the function 2[x/sinx6/5+x/tanx3/5] bounded by the function [...] Read more.
This paper established a new high precision Wilker-type inequality with fractional powers for the function 2[x/sinx6/5+x/tanx3/5] bounded by the function x6tanx/x5/4. Full article
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