New sharp bounds for sinc and hyperbolic sinc functions via cos and cosh functions

Huy, Duong Quoc; Hieu, Phan Trung; Van, Doan Thi Thuy

doi:10.1007/s13370-024-01185-6

Afr. Mat.

2024

DOI: 10.1007/s13370-024-01185-6

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New sharp bounds for sinc and hyperbolic sinc functions via cos and cosh functions

Duong Quoc Huy,

Phan Trung Hieu,

Doan Thi Thuy Van

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2024

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Cited by 2 publications

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The best possible constants approach for Wilker-Cusa-Huygens inequalities via stratification

Banjac,

Malesevic,

Micovic

et al. 2024

Appl Anal Discrete Math

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The best possible constants approach for Wilker-Cusa-Huygens inequalities via stratification

Banjac,

Malesevic,

Micovic

et al. 2024

Appl Anal Discrete Math

View full text Add to dashboard Cite

show abstract

A Parametric Method for Proving Some Analytic Inequalities

Malešević,

Mićović,

Mihailović

2024

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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.

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New sharp bounds for sinc and hyperbolic sinc functions via cos and cosh functions

Cited by 2 publications

References 20 publications

The best possible constants approach for Wilker-Cusa-Huygens inequalities via stratification

The best possible constants approach for Wilker-Cusa-Huygens inequalities via stratification

A Parametric Method for Proving Some Analytic Inequalities

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