Coincident-point rigidity in normed planes

Geometric clustering in normed planes

Given two sets of points A and B in a normed plane, we prove that there are two linearly separable sets A′ and B′ such that diam(A′) ≤ diam(A), diam(B′) ≤ diam(B), and A′ ∪B′ = A ∪B. This extends a result for the Euclidean distance to symmetric convex distance functions. As a consequence, some Euclidean k-clustering algorithms are adapted to normed planes, for instance, those that minimize the ...

On bisectors in normed planes

In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position of two given points with respect to the shape of the unit circle, the following holds: the bisector of a non-strict pair of points consists of two cones and a curve, which has properties similar to those of bisectors...

Minimum Steiner Trees in Normed Planes

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. In this note we investigate various properties of minimum Steiner trees in normed planes, i.e., where the "unit disk" is an arbitrary compact convex centrally symmetric domain D having nonempty interior. We show that if the boundary of D is strictly convex and di...

The local Steiner problem in normed planes

Coincident point and fixed point results for three self mappings in cone metric spaces

In this attempt we proved results on points of coincidence and common xed points for three selfmappings satisfying generalized contractive type conditions in cone metric spaces. Our results gen-eralizes some previous known results in the literature (eg. [5], [6])