G-metrički prostori

master's thesis

• Author: Ana Arhanić
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Franka Miriam Brückler (član povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Committee member: Slaven Kožić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-07-21, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U diplomskom radu definirali smo \(G\)-metriku i dokazali njezina najbitnija svojstva koja smo koristil tijekom cijelog rada. Konstruirali smo \(G\)-metriku iz metrike, ali i metriku iz \(G\)-metrike. Dokazali smo i nekoliko dokaza vezanih uz konvergenciju i potpunost \(G\)-metričkog prostora. Za kraj smo proučavali teoreme o fiksnoj točki. Dokazali smo Banachov teorem o fiksnoj točki, teorem o fiksnoj točki u \(G\)-metričkom prostoru i povezano s tim dijelom, još nekoliko teorema.

Abstract (english)

In the thesis, we defined \(G\)-metric and proved its most important properties that we used throughout the paper. We constructed a \(G\)-metric from the metric, but also a metric from the \(G\)-metric. We have also proved several proofs related to the convergence and completeness of the \(G\)-metric space. Finally, we studied fixed point theorems. We have proved Banach 's fixed point theorem, the fixed point theorem in \(G\)-metric space and, in connection with this part, several other theorems.

• Keywords: G-metrički prostori; teoremi o fiksnoj točki; Banachov teorem
• Keywords (english): G-metric spaces; fixed point theorems; Banach's theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:859513
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-11-12 16:06:16