Novel Multivariate Integral Operators Incorporating Trigonometric Transformations
The creation of new nonlinear multivariate integral operators is motivated by the need for mathematical tools that can handle the complex interdependencies that naturally arise in contemporary applications. From an abstract scientific point of view, it is also necessary to develop new operator theor...
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| Format: | Article |
| Language: | English |
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Mathyze Publishers
2024-04-01
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| Series: | Pan-American Journal of Mathematics |
| Online Access: | https://mathyze.com/index.php/pajm/article/view/178 |
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| _version_ | 1849433511021248512 |
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| author | Christophe Chesneau |
| author_facet | Christophe Chesneau |
| author_sort | Christophe Chesneau |
| collection | DOAJ |
| description | The creation of new nonlinear multivariate integral operators is motivated by the need for mathematical tools that can handle the complex interdependencies that naturally arise in contemporary applications. From an abstract scientific point of view, it is also necessary to develop new operator theories beyond existing ones to offer original research perspectives. This article contributes to these complementary aspects. We present two nonlinear multivariate integral operators that have the particularity of incorporating trigonometric transformations of the main function. Thanks to their trigonometric nature, they completely stand out from existing operators, offering a new and complete framework. Therefore, we take advantage of advanced mathematical techniques for trigonometric functions to address the challenges they pose. In particular, we show that they have manageable integrals and series expansions, that they are solutions of specific differential and functional equations, and that they are involved in general inequalities of various types (Hölder-type, convex-type, etc.). In the application part, we use some of these properties to propose a wide collection of trigonometric inequalities that are both original and precise. Figures are produced to illustrate them for a direct visual check. |
| format | Article |
| id | doaj-art-8ff4bb5904e54ebd96ed611d2a152344 |
| institution | Kabale University |
| issn | 2832-4293 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Mathyze Publishers |
| record_format | Article |
| series | Pan-American Journal of Mathematics |
| spelling | doaj-art-8ff4bb5904e54ebd96ed611d2a1523442025-08-20T03:27:01ZengMathyze PublishersPan-American Journal of Mathematics2832-42932024-04-013010.28919/cpr-pajm/3-1148Novel Multivariate Integral Operators Incorporating Trigonometric TransformationsChristophe Chesneau0University of Caen-Normandie, FranceThe creation of new nonlinear multivariate integral operators is motivated by the need for mathematical tools that can handle the complex interdependencies that naturally arise in contemporary applications. From an abstract scientific point of view, it is also necessary to develop new operator theories beyond existing ones to offer original research perspectives. This article contributes to these complementary aspects. We present two nonlinear multivariate integral operators that have the particularity of incorporating trigonometric transformations of the main function. Thanks to their trigonometric nature, they completely stand out from existing operators, offering a new and complete framework. Therefore, we take advantage of advanced mathematical techniques for trigonometric functions to address the challenges they pose. In particular, we show that they have manageable integrals and series expansions, that they are solutions of specific differential and functional equations, and that they are involved in general inequalities of various types (Hölder-type, convex-type, etc.). In the application part, we use some of these properties to propose a wide collection of trigonometric inequalities that are both original and precise. Figures are produced to illustrate them for a direct visual check.https://mathyze.com/index.php/pajm/article/view/178 |
| spellingShingle | Christophe Chesneau Novel Multivariate Integral Operators Incorporating Trigonometric Transformations Pan-American Journal of Mathematics |
| title | Novel Multivariate Integral Operators Incorporating Trigonometric Transformations |
| title_full | Novel Multivariate Integral Operators Incorporating Trigonometric Transformations |
| title_fullStr | Novel Multivariate Integral Operators Incorporating Trigonometric Transformations |
| title_full_unstemmed | Novel Multivariate Integral Operators Incorporating Trigonometric Transformations |
| title_short | Novel Multivariate Integral Operators Incorporating Trigonometric Transformations |
| title_sort | novel multivariate integral operators incorporating trigonometric transformations |
| url | https://mathyze.com/index.php/pajm/article/view/178 |
| work_keys_str_mv | AT christophechesneau novelmultivariateintegraloperatorsincorporatingtrigonometrictransformations |