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dc.contributor.authorDenız, Ali
dc.contributor.authorKoçak, Şahin
dc.contributor.authorOzdemır, Yunus
dc.contributor.authorRatıu, Andrei
dc.contributor.authorÜreyen, Adem Ersin
dc.date.accessioned2019-10-20T14:28:33Z
dc.date.available2019-10-20T14:28:33Z
dc.date.issued2013
dc.identifier.issn1300-0098
dc.identifier.urihttp://www.trdizin.gov.tr/publication/paper/detail/TVRVd01UVTJOZz09
dc.identifier.urihttps://hdl.handle.net/11421/18172
dc.description.abstractThe question of Minkowski measurability of fractals is investigated for different situations by various authors, notably by M. Lapidus. In dimension one it is known that the attractor of an IFS consisting of similitudes (and satisfying a certain open set condition) is Minkowski measurable if and only if the IFS is of non-lattice type and it was conjectured that this would be true also in higher dimensions. Half of this conjecture was proved by Gatzouras in 2000, who showed that the attractor of an IFS (satisfying the open set condition) is Minkowski measurable if the IFS is of non-lattice type. M. Lapidus and E. Pearse give in their recent work in 2010 a sketch of proof of this conjecture. We give in this work, under certain conditions needed for the application of the Lapidus-Pearse theory, a complete detailed proof of this conjecture, filling in the gaps and resolving the difficulties appearing in their sketch of proof. We also give an alternative proof of Gatzouras' theorem under the same restrictions and give an explicit formula for the Minkowski content.en_US
dc.description.abstractThe question of Minkowski measurability of fractals is investigated for different situations by various authors, notably by M. Lapidus. In dimension one it is known that the attractor of an IFS consisting of similitudes (and satisfying a certain open set condition) is Minkowski measurable if and only if the IFS is of non-lattice type and it was conjectured that this would be true also in higher dimensions. Half of this conjecture was proved by Gatzouras in 2000, who showed that the attractor of an IFS (satisfying the open set condition) is Minkowski measurable if the IFS is of non-lattice type. M. Lapidus and E. Pearse give in their recent work in 2010 a sketch of proof of this conjecture. We give in this work, under certain conditions needed for the application of the Lapidus-Pearse theory, a complete detailed proof of this conjecture, filling in the gaps and resolving the difficulties appearing in their sketch of proof. We also give an alternative proof of Gatzouras' theorem under the same restrictions and give an explicit formula for the Minkowski content.en_US
dc.language.isoengen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectMatematiken_US
dc.titleOn the Minkowski measurability of self-similar fractals in Rden_US
dc.typearticleen_US
dc.relation.journalTurkish Journal of Mathematicsen_US
dc.contributor.departmentAnadolu Üniversitesi, Fen Fakültesi, Matematik Bölümüen_US
dc.identifier.volume37en_US
dc.identifier.issue5en_US
dc.identifier.startpage830en_US
dc.identifier.endpage846en_US
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanıen_US]
dc.contributor.institutionauthorKoçak, Şahin
dc.contributor.institutionauthorÜreyen, Adem Ersin


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