PRILOG TEORIJI APSTRAKTNIH METRIČKIH PROSTORA

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PRILOG TEORIJI APSTRAKTNIH METRIČKIH PROSTORA

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dc.contributor.advisor Kadelburg, Zoran
dc.contributor.author Jovanović, Mirko
dc.date.accessioned 2017-04-27T16:42:42Z
dc.date.available 2017-04-27T16:42:42Z
dc.date.issued 2016
dc.identifier.uri http://hdl.handle.net/123456789/4458
dc.description.abstract This dissertation is the contribution to the Metric fixed point theory, the area that has recently been rapidly developing. It contains five chapters. The first chapter gives the proof of one already known lemma. This lemma is used in the proof of Banach’s theorem for orbital complete metric spaces. The second chapter contains the proofs of eight theorems, which generalize some known results from the theory of fixed points in metric spaces (Boyd-Wong’s, ´ Ciri´c ’ s, Pant’ s, and other). Some of these theorems are modifications of the known ones, while three are completely new. Three theorems are proven in the third chapter. They generalize the result of fixed point of mapping defined in compact metric space given by Nemytzki, as well as one generalization of Edelstein’s theorem. The proofs and stated corollaries of some theorems are original. Chapter four discusses b-metric spaces as a generalization of metric spaces. The generalization of Zamfirescu’s theorem of b-metric spaces is presented as well as some of its applications. A new result concerning weakly almost contractive mappings is also determined. Chapter five contains some new results in cone metric spaces. Two theorems are presented as the analogue of the same theorems in the setting of standard metric spaces. A completely new theorem is established which results in the Banach’s theorem in cone metric spaces whereby the cone does not need to be normal. A generalization of Fisher’s theorem in cone metric spaces over a regular cone is also proven. Almost all results in this dissertation are confirmed by corresponding examples, which explain how these results differ from the already known results. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2017-04-27T16:42:42Z No. of bitstreams: 1 Mirko_Jovanovic_dr.pdf: 1375536 bytes, checksum: 9c1365a64f5e140cfdcb0498cb64c232 (MD5) en
dc.description.provenance Made available in DSpace on 2017-04-27T16:42:42Z (GMT). No. of bitstreams: 1 Mirko_Jovanovic_dr.pdf: 1375536 bytes, checksum: 9c1365a64f5e140cfdcb0498cb64c232 (MD5) Previous issue date: 2016 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title PRILOG TEORIJI APSTRAKTNIH METRIČKIH PROSTORA en_US
mf.author.birth-date 1952-10-31
mf.author.birth-place Jagodina en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srbin en_US
mf.subject.area Mathematical analysis en_US
mf.subject.keywords Cone metric space, normal cone, b-complete metric space, Banach’s contraction, generalized contraction, fixed point, weakly compatible, weakly semi compatible, weakly commutative, the sequence of bounded variation en_US
mf.subject.subarea Nonlinear functional analysis en_US
mf.contributor.committee Kadelburg, Zoran
mf.contributor.committee Aranđelović, Ivan
mf.contributor.committee Cakić, Nenad
mf.university.faculty Mathematical Faculty en_US
mf.document.references 63 en_US
mf.document.pages 122 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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