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A two-parameter control for contractive-like multivalued mappingsRepovš, Dušan, 1954-Predložen je splošen pristop k definiciji skrčitvam podobne večlične preslikave ▫$F$▫, ki se izogne kakršnikoli uporabi Hausdorffove razdalje med množicama ▫$F(x)$▫ in ▫$F(y)$▫. Dokazani so različni ... izreki o negibnih točkah z dvoparametersko kontrolo funkcije razdalje ▫$d_F(x) = {\rm dist}(x,F(x))$▫ med točko ▫$x \in X$▫ in vrednostjo ▫$F(x) \subset X$▫. Pri tem sta oba parametra numerični funkciji. Prvi parameter ▫$\alpha \colon [0,+\infty) \to [1,+\infty)$▫ kontrolira razdaljo med ▫$x$▫ in neko ustrezno točko ▫$y \in F(x)$▫ v primerjavi z ▫$d_F(x)$▫, medtem ko drugi parameter ▫$\beta \colon [0,+\infty) \to [0,1)$▫ ocenjuje ▫$d_F(y)$▫ glede na ▫$d(x,y)$▫. Kaže, da so lepo harmonizirane relacije med ▫$\alpha$▫ and ▫$\beta$▫ zadostne za obstoj negibnih točk preslikave ▫$F$▫. Naši rezultati posplošujejo več znanih izrekov o negibnih točkahSource: 2010 International Conference on Topology and its Applications (Str. 1899-1905)Type of material - conference contributionPublish date - 2012Language - englishCOBISS.SI-ID - 16224857
Author
Repovš, Dušan, 1954-
Topics
matematika |
topologija |
poln metrični prostor |
večlična preslikava |
navzdol polzvezna funkcija |
skrčitev z zaprtimi vrednostmi |
Hausdorffova razdalja |
negibna točka preslikave |
mathematics |
topology |
complete metric space |
multivalued mapping |
lower semicontinuous function |
closed-valued contraction |
Hausdorff distance |
fixed point of a mapping
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