It was proved by M. Bonk, J. Heinonen and P. Koskela that the quasihyperbolic metric hyperbolizes (in the sense of Gromov) uniform metric spaces. In this paper we introduce a new metric that hyperbolizes all locally compact noncomplete metric spaces. The metric is generic in the sense that (1) it can be defined on any metric space; (2) it preserves the quasiconformal geometry of the space; (3) ...

This paper contains the equivalence between tvs-G cone metric and G-metric using a scalarization function $\zeta_p$, defined over locally convex Hausdorff topological vector space. ensures that most studies on existence uniqueness of fixed-point theorems space spaces are equivalent. We prove vector-valued version scalar-valued those spaces. Moreover, we present if real Banach is considered inst...

In this article we study metric spaces which admit polynomial diameter-volume inequalities for k-dimensional cycles. These generalize the notion of cone type inequalities introduced by M. Gromov in his seminal paper Filling Riemannian manifolds. In a first part we prove a polynomial isoperimetric inequality for k-cycles in such spaces, generalizing Gromov’s isoperimetric inequality of Euclidean...