Jarno Talponen

Convexity properties of quasihyperbolic balls on Banach spaces

We study the convexity and starlikeness of metric balls on Banach spaces when the metric is the quasihyperbolic metric or the distance ratio metric. In particular, problems related to these metrics on convex domains, and on punctured Banach spaces, are considered.

ON QUASIHYPERBOLIC GEODESICS IN BANACH SPACES

We study properties of quasihyperbolic geodesics on Banach spaces. For example, we show that in a strictly convex Banach space with the Radon-Nikodym property, the quasihy- perbolic geodesics are unique. We also give an example of a convex domain in a Banach space such that there is no geodesic between any given pair of points x,y ∈ . In addition, we prove that if X is a uniformly convex Banach space and its modulus of convexity is of a power type, then every geodesic of the quasihyperbolic metric, defined on a proper subdomain of X, is smooth.

On natural density, orthomodular lattices, measure algebras and non-distributive L^p spaces

In this note we first show, roughly speaking, that if

Note on Kadets Klee property and Asplund spaces

\mathcal {B}

Diameter 2 properties and convexity

B is a Boolean algebra included in the natural way in the collection

On the smoothness of quasihyperbolic balls

\mathcal {D}/_\sim