Menger curvature and Lipschitz parametrizations in metric spaces

Spaces of Lipschitz Functions on Metric Spaces

In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.

Fixed Points and Best Approximation in Menger Convex Metric Spaces

Nonexpansive mappings have been studied extensively in recent years by many authors.The first fixed point theorem of a general nature for nonlinear nonexpansive mappings in noncompact setting were proved independently by Browder [8] and Gohde [12]. Later on, Kirk [17] proved the same results under slightly weaker assumptions. A fundamental problem in fixed point theory of nonexpansive mappings ...

Generalized Distance and Common Fixed Point Theorems in Menger Probablistic Metric Spaces

A Menger Redux: Embedding Metric Spaces Isometrically in Euclidean Space

We present geometric proofs of Menger’s results on isometrically embedding metric spaces in Euclidean space. In 1928, Karl Menger [6] published the proof of a beautiful characterization of those metric spaces that are isometrically embeddable in the ndimensional Euclidean space E. While a visitor at Harvard University and the Rice Institute in Houston during the 1930-31 academic year, Menger ga...

A Contraction Theorem in Menger Probabilistic Metric Spaces

In this paper, we consider complete menger probabilistic quasimetric space and prove a common fixed point theorem for commuting maps in this space.