dc.contributor.author | Zheng, S. | |
dc.contributor.author | Yang Z-H. | |
dc.date.accessioned | 2017-06-22T14:09:28Z | |
dc.date.available | 2017-06-22T14:09:28Z | |
dc.date.issued | 2017-06-21 | |
dc.identifier.issn | 1660-5454 | |
dc.identifier.uri | http://hdl.handle.net/20.500.11824/691 | |
dc.description.abstract | Let $I_{\nu }\left( x\right) $ be the modified Bessel functions of the first
kind of order $\nu $, and $S_{p,\nu }\left( x\right) =W_{\nu }\left(
x\right) ^{2}-2pW_{\nu }\left( x\right) -x^{2}$ with $W_{\nu }\left(
x\right) =xI_{\nu }\left( x\right) /I_{\nu +1}\left( x\right) $. We achieve
necessary and sufficient conditions for the inequality $S_{p,\nu }\left(
x\right) <u$ or $S_{p,\nu }\left( x\right) >l$ to hold for $x>0$ by
establishing the monotonicity of $S_{p,\nu }(x)$ in $x\in \left( 0,\infty
\right) $ with $\nu >-3/2$. In addition, the best parameters $p$ and $q$ are
obtained to the inequality $W_{\nu }\left( x\right) <\left( >\right) p+\sqrt{%
x^{2}+q^{2}}$ for $x>0$. Our main achievements improve some known results,
and it seems to answer an open problem recently posed by Hornik and Gr\"{u}n
in [13]. | en_US |
dc.description.sponsorship | NSFC grant 11371050 and NSFC-ERC grant 11611530539. | en_US |
dc.format | application/pdf | en_US |
dc.language.iso | eng | en_US |
dc.rights | Reconocimiento-NoComercial-CompartirIgual 3.0 España | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/es/ | en_US |
dc.subject | modified Bessel functions of the first kind of order $\nu$ | en_US |
dc.subject | the ratio of modified Bessel functions | en_US |
dc.subject | monotonicity | en_US |
dc.subject | sharp bounds | en_US |
dc.title | Sharp bounds for the ratio of modified Bessel functions | en_US |
dc.type | info:eu-repo/semantics/article | en_US |
dc.relation.projectID | info:eu-repo/grantAgreement/EC/H2020/669689 | en_US |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | en_US |
dc.type.hasVersion | info:eu-repo/semantics/acceptedVersion | en_US |
dc.journal.title | Mediterranean Journal of Mathematics | en_US |