# A new approach to nonlinear singular integral operators depending on three parameters

Open Mathematics (2016)

• Volume: 14, Issue: 1, page 897-907
• ISSN: 2391-5455

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## Abstract

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In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , ${T}_{\lambda }\left(f;x,y\right)=\underset{{ℝ}^{2}}{\phantom{\rule{0.277778em}{0ex}}\int \int \phantom{\rule{0.277778em}{0ex}}}\left(t-x,s-y,f\left(t,s\right)\right)dsdt,\phantom{\rule{0.277778em}{0ex}}\left(x,y\right)\in {ℝ}^{2},\lambda \in \Lambda ,$ where Λ is a set of non-negative numbers with accumulation point λ0.

## How to cite

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Gumrah Uysal. "A new approach to nonlinear singular integral operators depending on three parameters." Open Mathematics 14.1 (2016): 897-907. <http://eudml.org/doc/287054>.

@article{GumrahUysal2016,
abstract = {In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , $\{T\_\lambda \}(f;x,y) = \iint \limits \_\{\{\mathbb \{R\}^2\}\} \{(t - x,s - y,f(t,s))dsdt,\;(x,y) \in \{\mathbb \{R\}^2\},\lambda \in \Lambda ,\}$ where Λ is a set of non-negative numbers with accumulation point λ0.},
author = {Gumrah Uysal},
journal = {Open Mathematics},
keywords = {Nonlinear integral operators; Generalized Lebesgue point; Weighted approximation; nonlinear integral operators; generalized Lebesgue point; weighted approximation},
language = {eng},
number = {1},
pages = {897-907},
title = {A new approach to nonlinear singular integral operators depending on three parameters},
url = {http://eudml.org/doc/287054},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Gumrah Uysal
TI - A new approach to nonlinear singular integral operators depending on three parameters
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 897
EP - 907
AB - In this paper, we present some theorems on weighted approximation by two dimensional nonlinear singular integral operators in the following form: T λ ( f ; x , y ) = ∬ R 2 ( t − x , s − y , f ( t , s ) ) d s d t , ( x , y ) ∈ R 2 , λ ∈ Λ , ${T_\lambda }(f;x,y) = \iint \limits _{{\mathbb {R}^2}} {(t - x,s - y,f(t,s))dsdt,\;(x,y) \in {\mathbb {R}^2},\lambda \in \Lambda ,}$ where Λ is a set of non-negative numbers with accumulation point λ0.
LA - eng
KW - Nonlinear integral operators; Generalized Lebesgue point; Weighted approximation; nonlinear integral operators; generalized Lebesgue point; weighted approximation
UR - http://eudml.org/doc/287054
ER -

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