On certain multidimensional nonlinear integrals

Authors : Özge ÖZALP GÜLLER, Gumrah UYSAL

Pages : 1356-1367

Doi:10.31801/cfsuasmas.762646

View : 18 | Download : 12

Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :The aim of the paper is to obtain generalized convergence results for nonlinear multidimensional integrals of the form: L_{η}insert ignore into journalissuearticles values(ω;x);=insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(ηⁿ);/insert ignore into journalissuearticles values(Ω_{n-1}););∫_{D}Kinsert ignore into journalissuearticles values(η|t-x|,ωinsert ignore into journalissuearticles values(t););dt. We will prove pointwise convergence of the family L_{η}insert ignore into journalissuearticles values(ω;x); as η→∞ at a fixed point x∈D which represents any generalized Lebesgue point of function ω∈L₁insert ignore into journalissuearticles values(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}insert ignore into journalissuearticles values(ω;x);=insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(ηⁿ);/insert ignore into journalissuearticles values(Ω_{n-1}););∫_{D}Kinsert ignore into journalissuearticles values(η|t-x|,ωinsert ignore into journalissuearticles values(t););dt. We will prove pointwise convergence of the family L_{η}insert ignore into journalissuearticles values(ω;x); as η→∞ at a fixed point x∈D which represents any generalized Lebesgue point of function ω∈L₁insert ignore into journalissuearticles values(D);, where D is an open bounded subset of Rⁿ. Moreover, we will consider the case D=Rⁿ.
Keywords : Taylor expansion, Generalized Lebesgue point, Pointwise convergence