Some tauberian theorems for weighted means of double integrals on R2+

Basit Öğe Kaydı
dc.authorid0000-0002-1754-1685en_US
dc.authorid0000-0002-2356-3987en_US
dc.contributor.authorFındık, Gökşen
dc.contributor.authorÇanak, İbrahim
dc.date.accessioned2024-07-12T20:46:35Z
dc.date.available2024-07-12T20:46:35Z
dc.date.issued2019en_US
dc.departmentFakülteler, İnsan ve Toplum Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractLet p(x) and q(y) be nondecreasing continuous functions on [0, ?) such that p(0) = q(0) = 0 and p(x), q(y) ? ? as x, y ? ?. For a locally integrable function f(x, y) on R 2 + = [0, ?) × [0, ?), we denote its double integral by F(x, y) = ? x 0 ? y 0 f(t, s)dtds and its weighted mean of type (?, ?) by t?,?(x, y) = ? x 0 ? y 0 ( 1 ? p(t) p(x) )? ( 1 ? q(s) q(y) )? f(t, s)dtds where ? > ?1 and ? > ?1. We say that ? ? 0 ? ? 0 f(t, s)dtds is integrable to L by the weighted mean method of type (?, ?) determined by the functions p(x) and q(x) if limx,y?? t?,?(x, y) = L exists. We prove that if limx,y?? t?,?(x, y) = L exists and t?,?(x, y) is bounded on R 2 + for some ? > ?1 and ? > ?1, then limx,y?? t?+h,?+k(x, y) = L exists for all h > 0 and k > 0. Finally, we prove that if ? ? 0 ? ? 0 f(t, s)dtds is integrable to L by the weighted mean method of type (1, 1) determined by the functions p(x) and q(x) and conditions p(x) p ? (x) ? y 0 f(x, s)ds = O(1) and q(y) q ? (y) ? x 0 f(t, y)dt = O(1) hold, then limx,y?? F(x, y) = L exists.en_US
dc.identifier.citationFındık, G., Çanak, İ. (2019). Some tauberian theorems for weighted means of double integrals on R2+. International Conference of Mathematical Sciences. s. 030019(1)-030019(3).en_US
dc.identifier.endpage030019-3en_US
dc.identifier.isbn978-0-7354-1816-5
dc.identifier.startpage030019-1en_US
dc.identifier.urihttps://aip.scitation.org/doi/10.1063/1.5095104
dc.identifier.urihttps://hdl.handle.net/20.500.12415/1879
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofInternational Conference of Mathematical Sciencesen_US
dc.relation.isversionof10.1063/1.5095104en_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY01338
dc.subjectDivergent integralsen_US
dc.subjectWeighted means of double integralsen_US
dc.subjectTauberian theorems and conditionsen_US
dc.titleSome tauberian theorems for weighted means of double integrals on R2+en_US
dc.typeArticle
dspace.entity.typePublication

Dosyalar

Koleksiyon

İnsan ve Toplum Bilimleri Fakültesi Koleksiyonu