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Further results on the neutrix composition of distributions involving the delta function and the function cosh(+)(-1) (x(1/r)

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dc.contributor.author Fisher, Brian
dc.contributor.author Taş, Kenan
dc.date.accessioned 2020-01-28T12:59:50Z
dc.date.available 2020-01-28T12:59:50Z
dc.date.issued 2019-01
dc.identifier.citation Fisher, Brian; Taş, Kenan, "Further results on the neutrix composition of distributions involving the delta function and the function cosh(+)(-1) (x(1/r)", Demonstratio Mathematica, Vol. 52, No. 1, pp. 249-255, (2019). tr_TR
dc.identifier.issn 0420-1213
dc.identifier.uri http://hdl.handle.net/20.500.12416/2366
dc.description.abstract The neutrix composition F(f(x)) of a distribution F(x) and a locally summable function f(x) is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {F-n(f(x))) is equal to h(x), where F-n(x) = F(x) * delta(n)(x) and {delta(n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function delta(x). The function cosh(+)(-1)(x + 1) is defined by cosh(+)(-1)(x+ 1) = H(x) cosh(-1)(vertical bar x vertical bar + 1), where H(x) denotes Heaviside's function. It is then proved that the neutrix composition delta((s))[cosh(+)(-1)(x(1/r) + 1)] exists and delta((s))[cosh(+)(-1)(x(1/r) + 1] = Sigma(s-1)(k=0) Sigma(kr+r-1)(j=0) Sigma(j)(i=0) (-1)(kr+r+s-j-1)r/2(j+2) ((kr + r -1)(j)) ((j)(i)) [(j - 2i + 1)(s) - (j - 2i -1)(s)]delta((k))(x) for r, s = 1, 2, .... Further results are also proved. Our results improve, extend and generalize the main theorem of [Fisher B., Al-Sirehy F., Some results on the neutrix composition of distributions involving the delta function and the function cosh(+)(-1) (x + 1), Appl. Math. Sci. (Ruse), 2014, 8(153), 7629-7640]. tr_TR
dc.language.iso eng tr_TR
dc.publisher Sciendo tr_TR
dc.relation.isversionof 10.1515/dema-2019-0021 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject Distribution tr_TR
dc.subject Dirac-Delta Function tr_TR
dc.subject Composition of Distributions tr_TR
dc.subject Neutrix tr_TR
dc.subject Neutrix Limit tr_TR
dc.title Further results on the neutrix composition of distributions involving the delta function and the function cosh(+)(-1) (x(1/r) tr_TR
dc.type article tr_TR
dc.relation.journal Demonstratio Mathematica tr_TR
dc.contributor.authorID 4971 tr_TR
dc.identifier.volume 52 tr_TR
dc.identifier.issue 1 tr_TR
dc.identifier.startpage 249 tr_TR
dc.identifier.endpage 255 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik - Bilgisayar Bölümü tr_TR


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