On Turán type inequalities for modified Bessel functions

By 'Arp'ad Baricz, Saminathan Ponnusamy. 2010

71 citations recorded by the source corpus.

In this note our aim is to point out that certain inequalities for modified Bessel func- tions of the first and second kind, deduced recently by Laforgia and Natalini, are in fact equiva- lent to the corresponding Turan type inequalities for these functions. Moreover, we present some new Turan type inequalities for the aforementioned functions and we show that their product is decreasing as a function of the order, which has application in the study of stability of radially symmetric solutions in a generalized FitzHugh-Nagumo equation in two spatial dimensions. At the end of this note a conjecture is posed, which may be of interest for further research.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/80423a3553f61e76548ce56562bb28b1c6b24f57

Citations in the corpus

• Inequalities for modified Bessel functions and their integrals (2012, unknown): “Baricz, Á, Jankov, D. and Pogány, T.K. Turán type inequalities for Krätzel functions, J. Math.”
• Long-Time Behaviour and Phase Transitions for the Mckean–Vlasov Equation on the Torus (2018, unknown): “[17,67]) to assert that I0(a)I2(a)− I1(a)(2) < 0 for a > 0.”
• The radius of starlikeness of normalized Bessel functions of the first kind (2012, unknown): “Moreover, it is known (see for example [3]) that the function r → rI ′ ν(r)/Iν(r) is increasing on (0,∞) for all ν > −1.”