Proper version of Cusa-Huygens' inequality and Djokvie's type inequality for parabolic trigonometric functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F26%3A00566093" target="_blank" >RIV/60162694:G43__/26:00566093 - isvavai.cz</a>
Result on the web
<a href="https://mia.ele-math.com/28-42/Proper-version-of-Cusa-Huygens-inequality-and-Djokvie-s-type-inequality-for-parabolic-trigonometric-functions" target="_blank" >https://mia.ele-math.com/28-42/Proper-version-of-Cusa-Huygens-inequality-and-Djokvie-s-type-inequality-for-parabolic-trigonometric-functions</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7153/mia-2025-28-42" target="_blank" >10.7153/mia-2025-28-42</a>

Result language
angličtina
Original language name
Proper version of Cusa-Huygens' inequality and Djokvie's type inequality for parabolic trigonometric functions
Original language description
This paper aims to investigate several inequalities for parabolic trigonometric functions (PTF). We solve an open problem of proving Cusa-Huygens’ inequality for PTF. Furthermore, we find indefinite integrals for PTF; consequently, we derive a tight approximation for a particular integral. Additionally, we develop Djokvie’s type inequality for PTF and discover a precise upper bound on the function sinp(x) + cosp(x) , where sinp(x) denotes parabolic sine and cosp(x) parabolic cosine.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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