Riku Klén

On Jordan type inequalities for hyperbolic functions

This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as and are proved.

Local convexity properties of quasihyperbolic balls in punctured space

This paper deals with local convexity properties of the quasihyperbolic metric in the punctured space. We consider convexity and starlikeness of the quasihyperbolic balls.

Lipschitz conditions, triangular ratio metric, and quasiconformal maps

The triangular ratio metric is studied in subdomains of the complex plane and Euclidean

Bernoulli inequality and hypergeometric functions

n

Close-to-convexity of quasihyperbolic and j-metric balls

-space. Various inequalities are proven for it. The main results deal with the behavior of this metric under quasiconformal maps. We also study the smoothness of metric disks with small radii.

Inclusion relations of hyperbolic type metric balls

Bernoulli type inequalities for functions of logarithmic type are given. These functions include, in particular, Gaussian hypergeometric functions in the zero-balanced case

SOME REMARKS ON THE CASSINIAN METRIC

F(a,b;a+b;x)\,.

Teichmüller's problem in space

We will consider close-to-convexity of the metric balls defined by the quasihyperbolic metric and the j-metric. We will show that the jmetric balls with small radii are close-to-convex in general subdomains of R n and the quasihyperbolic balls with small radii are close-to-convex in the punctured space.

Local convexity properties of balls in Apollonian and Seittenranta’s metrics

Inclusion relations of metric balls defined by the hyperbolic, the quasihyperbolic, the