Oona Rainio

activity

20222024

collaborators

Showing math.MGShow all

5 papers · 1 filter

math.MG2024

Inequalities for a new hyperbolic type metric

Oona Rainio

We study a new hyperbolic type metric recently introduced by Song and Wang. We present formulas for it in the upper half-space and the unit ball domains and find its sharp inequali…

math.MG2024

Inequalities for geometric mean distance metric

Oona Rainio

We study a hyperbolic type metric $h_{G, c}$ introduced by Dovgoshey, Hariri, and Vuorinen. We find the best constant $c > 0$ , for which this function $h_{G, c}$ is a metric in specifi…

math.MG2023

Intrinsic metrics defined with arithmetic and logarithmic mean values

Oona Rainio, Rahim Kargar

We introduce several new functions that measure the distance between two points $x$ and $y$ in a domain $G ⊊ R^{n}$ by using the arithmetic or the logarithmic mean of…

math.MG2023

Inequalities for the generalized point pair function

Oona Rainio

We study a new generalized version of the point pair function defined with a constant $α > 0$ . We prove that this function is a quasi-metric for all values of $α > 0$ , and compare it t…

math.MG2022

Inclusion properties of the triangular ratio metric balls

Oona Rainio

Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the $j^{*}$ -metric, and the distance ratio metric defined in the unit ball domain. S…