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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.
MSC:
49J40Variational methods including variational inequalities
47H10Fixed point theorems for nonlinear operators on topological linear spaces
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