On certain multidimensional nonlinear integrals
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.
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- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi