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    Convergence of Singular Integral Operators in Weighted Lebesgue Spaces
    (European Journal Pure & Applied Mathematics, 2017) Yilmaz, Mine Menekse; Uysal, Gumrah
    In this paper, the pointwise approximation to functions f epsilon L-1,(w) (a, b) by the convolution type singular integral operators given in the following form: L-lambda(f; x) = integral(b)(a) f(t) K(lambda()t-x)dt, x epsilon(a,b), lambda epsilon A subset of R-0(+) where (a,b) stands for arbitrary closed, semi closed or open bounded interval in R or R itself L-1,(w)(a,b) denotes the space of all measurable but non-integrable functions f for which vertical bar f/w vertical bar integrable on (a,b) and w : R R+ is a corresponding weight function, at mu-generalized Lebesgue point and the rate of convergenceat this point are studied.
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    A note on rate of convergence of double singular integral operators
    (Springer International Publishing Ag, 2014) Yilmaz, Mine Menekse; Uysal, Gumrah; Ibikli, Ertan
    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: L-lambda(f; x, y) = integral integral(D) f (s, t) H-lambda (s-x, t-y) ds dt, (x, y) is an element of D, where D = < a, b > x < c, d > (< a, b > x < c, d > is an arbitrary closed, semi-closed or open region in R-2) and lambda epsilon Lambda, Lambda is a set of non-negative numbers with accumulation point lambda(0). Also we provide an example to support these theoretical results.
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    A study on pointwise approximation by double singular integral operators
    (Springeropen, 2015) Uysal, Gumrah; Yilmaz, Mine Menekse; Ibikli, Ertan
    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: Lx(f;x,y) = integral integral(D)f(t,s)H-lambda(t-x,s-y)dt ds, (x,y) is an element of D, where D = < a, b > x < c,d > is an arbitrary closed, semi-closed or open region in R-2 and lambda is an element of Lambda, Lambda is a set of non-negative numbers with accumulation point lambda(0). Also we provide an example to justify the theoretical results. MSC: Primary 41A35; secondary 41A25