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It is shown that a Korovkin-type theorem does not hold in the weighted space of Lp−locally integrable functions on the whole real axis.

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In this paper we prove the pointwise convergence and the rate of pointwise convergence for a family of singular integral operators with radial kernel in two-dimensional setting in the following form:is an arbitrary closed, semi-closed or open region in R 2 ) and λ ∈ , is a set of non-negative numbers with accumulation point λ 0 . Also we provide an example to support these theoretical results.MSC: Primary 41A35; secondary 41A25

In the present paper, we estimate the rate of pointwise convergence of the Bézier Variant of Chlodowsky operators C n, for functions, defined on the interval extending infinity, of bounded variation. To prove our main result, we have used some methods and techniques of probability theory.

In the present work we prove the pointwise convergence and the rate of pointwise convergence for a family of singular integral operators with radial kernel in two-dimensional setting in the following form:is an arbitrary closed, semi-closed or open region in R 2 and λ ∈ , is a set of non-negative numbers with accumulation point λ 0 . Also we provide an example to justify the theoretical results. MSC: Primary 41A35; secondary 41A25

In this study, we present some results on the weighted pointwise convergence of a family of singular integral operators with radial kernels given in the following form: L k f ; x; y ð Þ ¼ ZZ R 2 f t; s ð ÞH k t À x; s À y ð Þ ds dt; x; y ð Þ 2 R 2 ; k 2 K; where K is a set of non-negative numbers with accumulation point k 0 , and the function f is measurable on R 2 in the sense of Lebesgue.