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http://dx.doi.org/10.11568/kjm.2018.26.3.483

SOME WEIGHTED APPROXIMATION PROPERTIES OF NONLINEAR DOUBLE INTEGRAL OPERATORS  

Uysal, Gumrah (Department of Computer Technologies Division of Technology of Information Security Karabuk University)
Mishra, Vishnu Narayan (Department of Mathematics Indira Gandhi National Tribal University)
Serenbay, Sevilay Kirci (Department of Mathematics Harran University)
Publication Information
Korean Journal of Mathematics / v.26, no.3, 2018 , pp. 483-501 More about this Journal
Abstract
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.
Keywords
Generalized Lipschitz condition; Weighted pointwise convergence; Rate of convergence;
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