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dc.contributor.authorZheng S.en_US
dc.contributor.authorYang Z-H.en_US
dc.date.accessioned2017-06-22T14:09:28Z
dc.date.available2017-06-22T14:09:28Z
dc.date.issued2017-06-21
dc.identifier.issn1660-5454
dc.identifier.urihttp://hdl.handle.net/20.500.11824/691
dc.description.abstractLet $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.sponsorshipNSFC grant 11371050 and NSFC-ERC grant 11611530539.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherMediterranean Journal of Mathematicsen_US
dc.relationinfo:eu-repo/grantAgreement/EC/H2020/669689en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectmodified Bessel functions of the first kind of order $\nu$en_US
dc.subjectthe ratio of modified Bessel functionsen_US
dc.subjectmonotonicityen_US
dc.subjectsharp boundsen_US
dc.titleSharp bounds for the ratio of modified Bessel functionsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/acceptedVersionen_US


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