The aim of the paper is to obtain generalized convergence results for nonlinear multidimensional integrals of the form:
L_{η}(ω;x)=((ηⁿ)/(Ω_{n-1}))∫_{D}K(η|t-x|,ω(t))dt.
We will prove pointwise convergence of the family L_{η}(ω;x) as η→∞ at a fixed point x∈D which represents any generalized Lebesgue point of function ω∈L₁(D), where D is an open bounded subset of Rⁿ. Moreover, we will consider the case D=Rⁿ.
The aim of the paper is to obtain generalized convergence results for nonlinear multidimensional integrals of the form:
L_{η}(ω;x)=((ηⁿ)/(Ω_{n-1}))∫_{D}K(η|t-x|,ω(t))dt.
We will prove pointwise convergence of the family L_{η}(ω;x) as η→∞ at a fixed point x∈D which represents any generalized Lebesgue point of function ω∈L₁(D), where D is an open bounded subset of Rⁿ. Moreover, we will consider the case D=Rⁿ.
Taylor expansion Generalized Lebesgue point Pointwise convergence
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Yayımlanma Tarihi | 31 Aralık 2020 |
Gönderilme Tarihi | 2 Temmuz 2020 |
Kabul Tarihi | 18 Eylül 2020 |
Yayımlandığı Sayı | Yıl 2020 Cilt: 69 Sayı: 2 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
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