Repository logo
 

Generalized Metrics

dc.contributor.advisorTymchatyn, Edward
dc.contributor.committeeMemberSrinivasan, Raj
dc.contributor.committeeMemberSzmigielski , Jacek
dc.contributor.committeeMemberMartin, John
dc.contributor.committeeMemberDutchyn, Christopher
dc.creatorAssaf, Samer
dc.date.accessioned2016-07-18T20:42:48Z
dc.date.available2016-07-18T20:42:48Z
dc.date.created2016-06
dc.date.issued2016-07-11
dc.date.submittedJune 2016
dc.date.updated2016-07-18T20:42:49Z
dc.description.abstractA distance on a set is a comparative function. The smaller the distance between two elements of that set, the closer, or more similar, those elements are. Fr\'echet axiomatized the notion of distance into what is today known as a metric. In this thesis we study several generalizations of Fr\'echet's axioms. These include partial metric, strong partial metric, partial $n-\mathfrak{M}$etric and strong partial $n-\mathfrak{M}$etric. Those generalizations allow for negative distances, non-zero distances between a point and itself and even the comparison of $n-$tuples. We then present the scoring of a DNA sequence, a comparative function that is not a metric but can be modeled as a strong partial metric. \\\indent Using the generalized metrics mentioned above we create topological spaces and investigate convergence, limits and continuity in them. As an application, we discuss contractiveness in the language of our generalized metrics and present Banach-like fixed, common fixed and coincidence point theorems.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10388/7351
dc.subjectPartial metric
dc.subjectn-Metric
dc.titleGeneralized Metrics
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics and Statistics
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Saskatchewan
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

Files

Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
ASSAF-DISSERTATION-2016.pdf
Size:
599.53 KB
Format:
Adobe Portable Document Format
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
LICENSE.txt
Size:
2.27 KB
Format:
Plain Text
Description: