• Korean Journal of Mathematics
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• v.26 no.3
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• pp.483-501
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• 2018

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.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.15-28
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• 2018

In this paper, we introduce a Stancu type generalization of genuine LupaŞ-Beta operators of integral type. We establish some moment estimates and the direct results in terms of classical modulus of continuity, Voronovskaja-type asymptotic theorem, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Lastly, we propose a king type modification of these operators to obtain better estimates.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.337-343
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• 2006

In the present paper we shall prove that on a foundation *-semigroup S with an identity and with a locally bounded Borel measurable weight function ${\omega}$, the pointwise convergence and the uniform convergence of a sequence of ${\omega}$-bounded exponentially convex functions on S which are also continuous at the identity are equivalent.