dc.contributor.author Zheng S. en_US dc.contributor.author Yang Z-H. en_US 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 en_US 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 $S_{p,\nu }\left( x\right) l$ 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]. 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.publisher Mediterranean Journal of Mathematics en_US dc.relation info:eu-repo/grantAgreement/EC/H2020/669689 en_US dc.rights info:eu-repo/semantics/openAccess 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.type info:eu-repo/semantics/acceptedVersion en_US
﻿

### This item appears in the following Collection(s)

Except where otherwise noted, this item's license is described as info:eu-repo/semantics/openAccess