Functional inequalities involving Bessel and modified Bessel functions of the first kind

By 'Arp'ad Baricz. 2008

83 citations recorded by the source corpus.

Abstract In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turan and Lazarevic-type inequalities for the confluent hypergeometric functions.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3d784aa50dd79415f209d04870a9c84ec6a61511

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On a product of modified Bessel functions (2008, background): “For more details on Turán type inequalities the interested reader is referred to the papers [2], [3], [4], [5], [8], [9], [10], [15] and to the references therein.”
Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems (2009, methodology): “20) was generalized in [5] to modified Bessel functions.”
Starlikeness and convexity of generalized Bessel functions (2010, background): “254] or 9 ), and consequently, we have On the other hand, it is known [ 6 , p.”
A note on Turán type and mean inequalities for the Kummer function (2009, background): “Inequalities involving contiguous Kummer confluent hypergeometric functions of the form Φ(a ± ν, c ± ν, x) and Φ(a, c ± ν, x) were presented in Theorem 2 of [4] and Theorem 2.”
Turán type inequalities for hypergeometric functions (2008, background): “This classical result has been extended in several directions: ultraspherical, Laguerre and Hermite polynomials [16], Jacobi polynomials [10, 11], general class of polynomials [9], Bessel functions of the first kind [15], modified Bessel functions of the first kind [6, 13, 18], and so forth.”
Log-convexity and log-concavity of hypergeometric-like functions (2009, background): “Proof. Statements a) and the part of b) for a,x > 0 follow from Theorem 3. The claim c) for positive x and a ≥ c > 0 was proved by Baricz in [ Baricz1 , Theorem 2]. By the Kummer transformation this yields b) for negative x and a 0 gives the part of c) with x Baricz1 , Baricz2, Baricz3, HVV, Bord”
On Turán type inequalities for modified Bessel functions (2010, methodology): “Inequality (10), which holds for all ν > −1 and u > 0, was proved using different arguments in 1951 by Thiruvenkatachar and Nanjundiah [34] for ν > −1, in 1991 by Joshi and Bissu [24] for ν ≥ 0, and recently by the first author [4, 8] for ν > −1.”
Bounds for modified Bessel functions of the first and second kinds (2010, background): “In [15] the case when x ∈ [−jν,1, jν,1] was settled by Baricz.”