關(guān)于概率度量空間中非線性算子不動點(diǎn)問題的研究.pdf

1、南昌大學(xué)碩士學(xué)位論文關(guān)于概率度量空間中非線性算子不動點(diǎn)問題的研究姓名：代愛蓮申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：朱傳喜20081101ABSTRACTThestudvofnonlinearoperatorscansolvemanyproblemsinsomesubjects，suchaSengineenng，physics，biologymedicine孤ds0onInprobabin皸記mem‘ispace，thedistanc

2、ebe倆een鉚0elementsismeasuredbyadistributionfunctionand二ordinarymetricspacecanbeviewedasaspecialcaseofap曲擷1i吼論眥眥spaceSo，thestudyofnonlinearoperatorsinprobablisticmetricspace1sslgIll脅nthlthispaper，theproblemsoffixedpointofn

3、onlinearoperatorsarestudiedlt1sdividedintothefollowingfoursections，lnchapterone，thebacl【鏟oundsandcurrentsituationofoperatortheorymPM。spacesareintroducedandthepreliminariesofPM。Spacesare咖en‘hchaptertwo，theproblemsoffixedp

4、ointofnonlinearoperatorsinprobabIistlcmetricspacewasdiscussed，andtheexistenceanduniquenesstheoremsoffixedpointforIlonlinearmultiplevaluedoperatorsandcompoundnonlinearsin酉eValuedoperatorsareproved，andsomecorollariesareobt

5、ained一hlchapterthree，utilizingtheconceptofpartialorderinprobabilisticmetrlcspacet0discllsstheexitence’sproblemsoffixedpoint，theoremsforfixedpoiIltalldconunonfixedpointofmonotonyincreasingandmonotonydecreasingoperatorsare

6、0btainedAtthes鋤etime，bythemethodsofpattialordersometheoremstorcommonfixedpointofthesquenceofmultiplevaluedoperatorsaregotIIlchapterfourthetypcsofcontractivemappingsinintuitionisticMengcfPM。spaceandconemetficspacearediscu