Certain inequalities for the modified Bessel-type function
Abstract We establish some new inequalities for the modified Bessel-type function λν,σ(β)(x) $\lambda _{\nu ,\sigma }^{(\beta )} (x )$ studied by Glaeske et al. [in J. Comput. Appl. Math. 118(1–2):151–168, 2000] as the kernel of an integral transformation that modifies Krätzel’s integral transformat...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-1974-1 |
| _version_ | 1828886427870429184 |
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| author | Min-Jie Luo Ravinder Krishna Raina |
| author_facet | Min-Jie Luo Ravinder Krishna Raina |
| author_sort | Min-Jie Luo |
| collection | DOAJ |
| description | Abstract We establish some new inequalities for the modified Bessel-type function λν,σ(β)(x) $\lambda _{\nu ,\sigma }^{(\beta )} (x )$ studied by Glaeske et al. [in J. Comput. Appl. Math. 118(1–2):151–168, 2000] as the kernel of an integral transformation that modifies Krätzel’s integral transformation. The inequalities obtained are closely related to the generalized Hurwitz–Lerch zeta function and complementary incomplete gamma function. We also deduce some useful inequalities for the modified Bessel function of the second kind Kν(x) $K_{\nu } (x )$ and Mills’ ratio M(x) $\mathsf{M} (x )$ as worthwhile applications of our main results. |
| first_indexed | 2024-12-13T11:45:40Z |
| format | Article |
| id | doaj.art-747d4eb2148e479b9b589304a006fe3f |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-13T11:45:40Z |
| publishDate | 2019-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-747d4eb2148e479b9b589304a006fe3f2022-12-21T23:47:32ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-01-012019111510.1186/s13660-019-1974-1Certain inequalities for the modified Bessel-type functionMin-Jie Luo0Ravinder Krishna Raina1Department of Mathematics, East China Normal UniversityM.P. University of Agriculture and TechnologyAbstract We establish some new inequalities for the modified Bessel-type function λν,σ(β)(x) $\lambda _{\nu ,\sigma }^{(\beta )} (x )$ studied by Glaeske et al. [in J. Comput. Appl. Math. 118(1–2):151–168, 2000] as the kernel of an integral transformation that modifies Krätzel’s integral transformation. The inequalities obtained are closely related to the generalized Hurwitz–Lerch zeta function and complementary incomplete gamma function. We also deduce some useful inequalities for the modified Bessel function of the second kind Kν(x) $K_{\nu } (x )$ and Mills’ ratio M(x) $\mathsf{M} (x )$ as worthwhile applications of our main results.http://link.springer.com/article/10.1186/s13660-019-1974-1Čebyšev inequalityGeneralized Hurwitz–Lerch zeta functionHölder’s inequalityIncomplete gamma functionMills’ ratio |
| spellingShingle | Min-Jie Luo Ravinder Krishna Raina Certain inequalities for the modified Bessel-type function Journal of Inequalities and Applications Čebyšev inequality Generalized Hurwitz–Lerch zeta function Hölder’s inequality Incomplete gamma function Mills’ ratio |
| title | Certain inequalities for the modified Bessel-type function |
| title_full | Certain inequalities for the modified Bessel-type function |
| title_fullStr | Certain inequalities for the modified Bessel-type function |
| title_full_unstemmed | Certain inequalities for the modified Bessel-type function |
| title_short | Certain inequalities for the modified Bessel-type function |
| title_sort | certain inequalities for the modified bessel type function |
| topic | Čebyšev inequality Generalized Hurwitz–Lerch zeta function Hölder’s inequality Incomplete gamma function Mills’ ratio |
| url | http://link.springer.com/article/10.1186/s13660-019-1974-1 |
| work_keys_str_mv | AT minjieluo certaininequalitiesforthemodifiedbesseltypefunction AT ravinderkrishnaraina certaininequalitiesforthemodifiedbesseltypefunction |