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\(Q\)-functions on quasimetric spaces and fixed points for multivalued maps. (English) Zbl 1215.49016
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.

49J40 Variational inequalities
47H10 Fixed-point theorems
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