Korean J. Math. Vol. 26 No. 3 (2018) pp.483-501
DOI: https://doi.org/10.11568/kjm.2018.26.3.483

Some weighted approximation properties of nonlinear double integral operators

Main Article Content

Gumrah Uysal
Vishnu Narayan Mishra
Sevilay Kirci Serenbay


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 }\left( f;x,y\right) =\underset{\mathbb{R}^{2}}{\iint }K_{\eta
}\left( t-x,s-y,f\left( t,s\right) \right) dsdt,\text{ }\left( x,y\right)
\in \mathbb{R}^{2},\text{ }\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.

Article Details


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