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SOME WEIGHTED APPROXIMATION PROPERTIES OF NONLINEAR DOUBLE INTEGRAL OPERATORS
Uysal, Gumrah,Mishra, Vishnu Narayan,Serenbay, Sevilay Kirci The Kangwon-Kyungki Mathematical Society 2018 한국수학논문집 Vol.26 No.3
In this paper, we present some recent results on weighted pointwise convergence and the rate of pointwise convergence for the family of nonlinear double singular integral operators in the following form: $$T_{\eta}(f;x,y)={\int}{\int\limits_{{\mathbb{R}^2}}}K_{\eta}(t-x,\;s-y,\;f(t,s))dsdt,\;(x,y){\in}{\mathbb{R}^2},\;{\eta}{\in}{\Lambda}$$, where the function $f:{\mathbb{R}}^2{\rightarrow}{\mathbb{R}}$ is Lebesgue measurable on ${\mathbb{R}}^2$ and ${\Lambda}$ is a non-empty set of indices. Further, we provide an example to support these theoretical results.