Geodesic
About one quasi-metric space
Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1285-1292 Cet article a éte moissonné depuis la source Math-Net.Ru

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The ${M}$-space $(X, \rho)$ is defined as a non-empty set $X$ with distance $\rho: X^2 \to \mathbb {R}_+$ satisfying the axiom of identity and the weakened triangle inequality. The ${M}$-space $(X, \rho)$ belongs to the class of $f$-quasi-metric spaces, and the map $\rho$ may not be $(c_1, c_2)$-quasi-metric for any values of $c_1, \, c_2;$ and $(c_1, c_2) $-quasi-metric space may not be an ${M}$-space. The properties of the ${M}$-space are investigated. An extension of the Krasnosel'skii theorem about a fixed point of a generally contracting map to the ${M}$-space is obtained.
Keywords: quasi-metric, triangle inequality, topology, fixed point, generalized contraction. 
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T. V. Zhukovskaya; E. S. Zhukovskiy. About one quasi-metric space. Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1285-1292. http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a8/

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