非對(duì)稱度量空間的完備性問(wèn)題研究.pdf

1、Y1213994學(xué)校代碼：10488學(xué)號(hào)：05lt)8014烈凄科手妻夫哮碩士學(xué)位論文題目非對(duì)稱度量空間的完備性問(wèn)題研究專一業(yè)研究方向姓，名導(dǎo)師應(yīng)用數(shù)學(xué)控制理論李文陳少白教授定稿日期：2007年11月10日第1I頁(yè)武漢科技大擎碩士學(xué)位論文AbstractAquasi—metricisadistancefunctionwhichsatisfiesthetriangleinequalitybutisnotsymmetric：itCanbet

2、houglftofasanasymmetricmetricSinceithasbeendrawningtheattentionsofmoreandmoreforeignresearchers，itsimportanceinthenonlinearsystemfieldhasbeenseenrecentlyThispapermainlyincludesthefollowingthreeaspects：1Basictheoryaboutqu

3、asimetricspacesFirstthemainresultsaboutquasimetricspacesobtainedbyothersaregatheredandmodifiedBasedonthose，thenotionofquasimetricproductspaceisputforward，andsomepropertiesarediscussed2CompletenessofquasimetricspacesFirst

4、lyseveralexamplesaboutuppercompletenessquasimetricspacesareobtainedSecondlyaquasimetricisputforward，whichisdefinedonthesetofallleftKLipschitzfunctionsonaquasimetricspacethatvanishatsome夙edpointandtheuppercompletenessofth

5、equasimetricisprovedThirdlytheleftandrightclosedballtheoremsinquasimetricspacesaregivenandtheequivalencebetweentheleft(ringt)closedballtheoremsandtheupper(10wer)completenessofquasimetricspacesareprovedFinallythenotionofu

6、pperandlowercontractionofmappingbetweenquasimetricspacesisputforwardandtwofixedpointtheoremsinquasimetricspacesareobtained3OptimizationprobleminquasiuniformspacesFirstlyitisprovedbytheauthorthataquasiuniformspaceisToifan

7、donlyiftheintersectionofallentouragesofthequasiunifo眥姆isantisymmetricrelationSecondlybasedonthefactthattheintersectionofallentouragesofther0q哪imfomtyisapartialordersomeextremumsin瓦quasianiformspacearedefinedanditsbasicpr

8、opertiesarediscussedFinallythegeneralformofoptimizationproblemina瓦quasiuniformspaceisgivenandtheexistenceofeffectivesolutionofoptimizationproblemisprovedKeyWords：Quasimetricspace；uppercompleteness；瓦quasiuiformspace；optim