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Fractals of Generalized F-Hutchinson Operator in b-Metric Spaces
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology, Pakistan. (MAM)ORCID-id: 0000-0001-6516-3212
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-4554-6528
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0002-0865-7248
2016 (Engelska)Ingår i: Journal of Operators, ISSN 2314-5064, Vol. 2016, s. 9 pp-, artikel-id 5250394Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize, and extend various results in the existing literature.

Ort, förlag, år, upplaga, sidor
Hindawi Publishing Corporation, 2016. Vol. 2016, s. 9 pp-, artikel-id 5250394
Nyckelord [en]
fractals, attractor, iterated function system, F-contraction, b-metric space
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-33093DOI: 10.1155/2016/5250394OAI: oai:DiVA.org:mdh-33093DiVA, id: diva2:963083
Projekt
FUSIONTillgänglig från: 2016-09-08 Skapad: 2016-09-07 Senast uppdaterad: 2016-12-05Bibliografiskt granskad
Ingår i avhandling
1. Fixed points, fractals, iterated function systems and generalized support vector machines
Öppna denna publikation i ny flik eller fönster >>Fixed points, fractals, iterated function systems and generalized support vector machines
2016 (Engelska)Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

In this thesis, fixed point theory is used to construct a fractal type sets and to solve data classification problem. Fixed point method, which is a beautiful mixture of analysis, topology, and geometry has been revealed as a very powerful and important tool in the study of nonlinear phenomena. The existence of fixed points is therefore of paramount importance in several areas of mathematics and other sciences. In particular, fixed points techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory and physics. In Chapter 2 of this thesis it is demonstrated how to define and construct a fractal type sets with the help of iterations of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the context of b-metric space. This leads to a variety of results for iterated function system satisfying a different set of contractive conditions. The results unify, generalize and extend various results in the existing literature. In Chapter 3, the theory of support vector machine for linear and nonlinear classification of data and the notion of generalized support vector machine is considered. In the thesis it is also shown that the problem of generalized support vector machine can be considered in the framework of generalized variation inequalities and results on the existence of solutions are established.

Ort, förlag, år, upplaga, sidor
Västerås: Mälardalen University Press, 2016. s. 66
Serie
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 247
Nyckelord
support vector machine, fixed points, iterated function system, variational inequality
Nationell ämneskategori
Beräkningsmatematik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-33511 (URN)978-91-7485-302-5 (ISBN)
Presentation
2016-12-12, U2-016, Mälardalen University, Västerås, 14:15 (Engelska)
Opponent
Handledare
Projekt
FUSION
Tillgänglig från: 2016-11-09 Skapad: 2016-11-08 Senast uppdaterad: 2016-11-24Bibliografiskt granskad

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Nazir, TalatSilvestrov, Sergei

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Totalt: 53 träffar
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