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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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    On pointwise convergence of bivariate nonlinear singular integral operators
    (Academic Publication Council, 2017) Uysal, Gumrah; Yilmaz, Mine M.; Ibikli, Ertan
    In this paper, we present some theorems on pointwise convergence and the rate of pointwise convergence for the family of nonlinear bivariate singular integral operators of the following form: T(lambda()f;x,y) = integral integral(D) K-lambda (t-x,s-yf(t,s))dsdt, (x,y)is an element of D, lambda is an element of Lambda where f is a real valued and integrable function on a bounded arbitrary closed, semi-closed or open region D = x in R-2 or D = R-2 and Lambda is the set of non-negative indices with accumulation point lambda(0)
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    Results On Convergence of Three-Parameter Family of Singular Integral Operators with Radial Kernels
    (Amer Inst Physics, 2016) Uysal, Gumrah; Ibikli, Ertan
    In this work, we present extra results on the weighted pointwise convergence for a family of singular integral operators with radial kernels. Also, we present a theorem concerning the rate of pointwise convergence.
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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
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    Weighted approximation by double singular integral operators with radially defined kernels
    (Springer Heidelberg, 2016) Uysal, Gumrah; Ibikli, Ertan
    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-lambda(f; x, y) = integral integral(R2) f(t, s)H-lambda(t - x, s - y)ds dt, (x, y) is an element of R-2, lambda is an element of Lambda, where Lambda is a set of non-negative numbers with accumulation point lambda(0), and the function f is measurable on R-2 in the sense of Lebesgue.