Some Tauberian Theorems for Weighted Means of Double Integrals on R-+(2)
| dc.contributor.author | Findik, Goksen | |
| dc.contributor.author | Canak, Ibrahim | |
| dc.contributor.editor | Cakalli, H | |
| dc.contributor.editor | Kocinac, LDR | |
| dc.contributor.editor | Harte, R | |
| dc.contributor.editor | Cao, J | |
| dc.contributor.editor | Savas, E | |
| dc.contributor.editor | Ersan, S | |
| dc.contributor.editor | Yildiz, S | |
| dc.date.accessioned | 2019-10-27T09:47:43Z | |
| dc.date.available | 2019-10-27T09:47:43Z | |
| dc.date.issued | 2019 | |
| dc.department | Ege Üniversitesi | en_US |
| dc.description | International Conference of Mathematical Sciences (ICMS) -- JUL 31-AUG 06, 2018 -- Maltepe Univ, Istanbul, TURKEY | en_US |
| dc.description.abstract | Let p(x) and q(y) be nondecreasing continuous functions on [0, infinity) such that p(0) = q(0) = 0 and p(x), q(y) -> infinity as x, y -> infinity. For a locally integrable function f(x,y) on R-+(2) = [0, infinity) x [0, infinity), we denote its double integral by F(x,y) = integral(x)(0) integral(y)(0) f(t, s)dtds and its weighted mean of type (alpha, beta) by t(alpha,beta)(x,y) = integral(x)(0) integral(y)(0) (1- p(t)/p(x))(alpha)(1-q(s)/q(y))(beta) f(t, s)dtds where alpha > -1 and beta > -1. We say that integral(infinity)(0)integral(infinity)(0) f(t, s)dtds is integrable to L by the weighted mean method of type (alpha, beta) determined by the functions p(x) and q(x) if lim(x,y -> infinity) t(alpha,beta)(x, y) = L exists. We prove that if lim(x,y -> infinity )t(alpha,beta)(x, y) = L exists and t a p(x, y) is bounded on R-+(2) for some alpha > -1 and beta > -1, then lim(x,y -> infinity )t(alpha+h,beta+k)(x, y)= L exists for all h > 0 and k > 0. Finally, we prove that if integral(infinity)(0) integral(infinity)(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) integral(y)(0) f(x, s)ds = O(1) and q(y)/q'(y) integral(x)(0) f(t, y)dt = O(1) hold, then lim(x,y ->infinity) F(x, y) = L exists. | en_US |
| dc.identifier.doi | 10.1063/1.5095104 | |
| dc.identifier.isbn | 978-0-7354-1816-5 | |
| dc.identifier.issn | 0094-243X | |
| dc.identifier.uri | https://doi.org/10.1063/1.5095104 | |
| dc.identifier.uri | https://hdl.handle.net/11454/29438 | |
| dc.identifier.volume | 2086 | en_US |
| dc.identifier.wos | WOS:000472950300024 | en_US |
| dc.identifier.wosquality | N/A | en_US |
| dc.indekslendigikaynak | Web of Science | en_US |
| dc.language.iso | en | en_US |
| dc.publisher | Amer Inst Physics | en_US |
| dc.relation.ispartof | International Conference of Mathematical Sciences (Icms 2018) | en_US |
| dc.relation.ispartofseries | AIP Conference Proceedings | |
| dc.relation.publicationcategory | Konferans Öğesi - Uluslararası - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Divergent integrals | en_US |
| dc.subject | weighted means of double integrals | en_US |
| dc.subject | Tauberian theorems and conditions | en_US |
| dc.title | Some Tauberian Theorems for Weighted Means of Double Integrals on R-+(2) | en_US |
| dc.type | Conference Object | en_US |
