Let R+ = (0,âˆž) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 âˆˆ M, we say that a function f : R+ â†’ R+â€¦ (More)

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 toâ€¦ (More)

We study monotonicity and convexity properties of functions arising in the theory of elliptic integrals, and in particular in the case of a Schwartz-Christoffel conformal mapping from a half-plane toâ€¦ (More)

In geometric function theory, conformally invariant extremal problems often have expressions in terms of special functions. Such problems occur, for instance, in the study of change of euclidean andâ€¦ (More)

We study monotonicity and convexity properties of functions arising in the theory of elliptic integrals, and in particular in the case of a Schwartz-Christoffel conformal mapping from a half-plane toâ€¦ (More)

Most distortion theorems for K'-quasiconformal mappings in R", n > 2, depend on both n and K in an essential way, with bounds that become infinite as n tends to oo. The present authors obtainâ€¦ (More)

Jacobiâ€™s elliptic integrals and elliptic functions arise naturally from the SchwarzChristoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalizedâ€¦ (More)

Asymptotic expansion of the arithmetic-geometric mean is obtained and it is used to analyze inequalities and relations between arithmetic-geometric mean and other classical means. Mathematics subjectâ€¦ (More)

Jacobiâ€™s elliptic integrals and elliptic functions arise naturally from the SchwarzChristoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalizedâ€¦ (More)