Abstract. We present various new inequalities involving the logarithmic mean $ L(x,y)=(x-y)/(\log{x}-\log{y}) $, the identric mean $ I(x,y)=(1/e)(x^x/y^y)^{1/(x-y)} $, and the classical arithmetic… Expand

In this paper we obtain a monotoneity property for the gamma function that yields sharp asymptotic estimates for 17(x) as x tends to oc, thus proving a conjecture about 17(x).

In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the… Expand

In geometric function theory, generalized elliptic integrals and functions arise ?from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to… Expand

We find the greatest value α1 and α2, and the least values β1 and β2, such that the double inequalities α1S(a,b) + (1 − α1) A(a,b) < T(a,b) < β1S(a,b) + (1 − β1) A(a,b) and… Expand

Monotonicity and convexity properties of certain functions defined in terms of complete elliptic integrals are studied and sharp functional inequalities for these functions are obtained, thus… Expand

For $r \in (0,1)$ and $a \in (0,1)$ the authors consider the quotient of hypergeometric functions $$ \mu_a(r)\equiv c F(a,1-a;1;1-r^2)/F(a,1-a;1;r^2), $$ where the normalizing coefficient $c = \pi/(2… Expand