No abstract

No abstract

We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals and depending on a parameter , which contains an earlier result in the particular case .

The purpose of this paper is to study the notion of the quasihyperbolic volume and to find growth estimates for the quasihyperbolic volume of balls in a domain G ⊂ R n , in terms of the radii.

Please cite this article in press as: X. Zhang, Solution to a conjecture on the Legendre M -function with an application to the generalized modulus, J. Math. Anal. Appl. (2015), http://dx.Abstract. In this note we give a solution to a conjecture on the Legendre M -function proposed by Heikkala, Linden, Vamanamurthy and Vuorinen in the paper: Generalized elliptic integrals and the Legendre M -function, J. Math. Anal. Appl. 338 (2008), 223-243. As an application of this result, we obtain a functional inequality of the generalized modulus.