ElsevierAlegre Gil, MC.; Marín Molina, J. (2016). Modified w-distances on quasi-metric spaces and a fixed point theorem on complete quasi-metric spaces.
AbstractIn this paper we introduce the notion of modified w-distance (mw-distance) on a quasi-metric space which generalizes the concept of quasi-metric. We obtain a fixed point theorem for generalized contractions with respect to mw-distances on complete quasi-metric spaces.
We obtain a fixed point theorem for generalized contractions on complete quasi-metric spaces, which involves w-distances and functions of Meir-Keeler and Jachymski type. Our result generalizes in various directions the celebrated fixed point theorems of Boyd and Wong, and Matkowski. Some illustrative examples are also given. MSC: 47H10; 54H25; 54E50
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.
Based on a Junnila's paracompactness characterization we give a definition of pairwise paracompact space which permits us to prove that a bitopological space is quasi-metrizable if, and only if, it is a pairwise developable and pairwise paracompact space. An easy consequence of this result is the biquasi-metric form of the Morita metrization theorem. We also give some results on open mappings and strong quasi-metrics.1980 Mathematics subject classification (Amer. Math. Soc): primary 54 E 35, 54 E 55; secondary 54 C 10, 54 D 18, 54 E 30.
By using a suitable modification of the notion of a w-distance we obtain some fixed point results for generalized contractive set-valued maps on complete preordered quasi-metric spaces. We also show that several distinguished examples of non-metrizable quasi-metric spaces and of cones of asymmetric normed spaces admit w-distances of this type. Our results extend and generalize some well-known fixed point theorems.
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