Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 603861, 10 pages
doi:10.1155/2011/603861
Research Article

𝑄 -Functions on Quasimetric Spaces and Fixed Points for Multivalued Maps

J. Marín, S. Romaguera, and P. Tirado

Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

Received 14 December 2010; Revised 26 January 2011; Accepted 31 January 2011

Academic Editor: Qamrul Hasan Ansari

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.

Abstract

We discuss several properties of 𝑄 -functions in the sense of Al-Homidan et al.. In particular, we prove that the partial metric induced by any 𝑇 0 weighted quasipseudometric space is a 𝑄 -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 𝑄 -function. In this context we also obtain some fixed point results for multivalued maps by using Bianchini-Grandolfi gauge functions.