Güller, Özge ÖzalpUysal, Gümrah2021-11-292021-11-292020-12-31https://doi.org/10.31801/cfsuasmas.762646http://hdl.handle.net/20.500.12575/76428The 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.enTaylor expansionGeneralized Lebesgue pointPointwise convergenceArticle692135613672618-6470