Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Copyright © 2011 J. Marín et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We discuss several properties of -functions in the sense of Al-Homidan et al.. In particular, we prove that the partial
metric induced by any weighted quasipseudometric space is a
-function and show that both the Sorgenfrey line and the Kofner
plane provide significant examples of quasimetric spaces for which
the associated supremum metric is a -function. In this context we
also obtain some fixed point results for multivalued maps by using
Bianchini-Grandolfi gauge functions.