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Zbl 1215.49016
Mar{\'\i}n, J.; Romaguera, S.; Tirado, P.
$Q$-functions on quasimetric spaces and fixed points for multivalued maps. (English)
[J] Fixed Point Theory Appl. 2011, Article ID 603861, 10 p. (2011). ISSN 1687-1812/e

Summary: We discuss several properties of $Q$-functions in the sense of Al-Homidan et al. 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.

MSC 2000:: *49J40 Variational methods including variational inequalities
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: $Q$-functions; quasimetric spaces; supremum metric; fixed point results for multivalued maps; Bianchini-Grandolfi gauge functions

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