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    ON SINGULAR INTEGRAL OPERATORS INVOLVING POWER NONLINEARITY
    (Kangwon-Kyungki Mathematical Soc, 2017) Almali, Sevgi Esen; Uysal, Gumrah; Mishra, Vishnu Narayan; Guller, Ozge Ozalp
    In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power non linearity given in the following form: T-lambda(f;x) = integral(b)(a) Sigma(n)(m=1) f(m)(t)K-lambda,K-m(x,t)dt, lambda epsilon Lambda, x epsilon (a, b), where A is an index set consisting of the non-negative real numbers, and n >= 1 is a finite natural number, at mu-generalized Lebesgue points of integrable function f epsilon L-1 (a, b). Here, f(m) denotes m - th power of the function f and (a, b) stands for arbitrary bounded interval in or I itself. We also handled the indicated problem under the assumption f epsilon L-1 (N)
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    RECENT OBSERVATIONS ON NONLINEAR TWO-PARAMETER SINGULAR INTEGRAL OPERATORS
    (Univ Prishtines, 2019) Tapiawala, Dipti; Uysal, Gumrah; Mishra, Vishnu Narayan
    In this paper, we present some theorems concerning weighted pointwise convergence of nonlinear singular integral operators of the form: (T(xi)f) (x) = integral(b)(a) K-xi (t - x, f(t)) dt, x is an element of (a, b), xi is an element of Xi, where (a, b) is a certain finite interval in R, Xi is a non-empty set of indices and f is measurable function on (a, b) in the sense of Lebesgue.
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    SOME WEIGHTED APPROXIMATION PROPERTIES OF NONLINEAR DOUBLE INTEGRAL OPERATORS
    (Kangwon-Kyungki Mathematical Soc, 2018) Uysal, Gumrah; Mishra, Vishnu Narayan; Serenbay, Sevilay Kirci
    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) = integral integral(RK)-K-2 eta (t - x, s - y, f (t, s)) dsdt, (x, y) is an element of R-2, eta is an element of Lambda, where the function f : R-2 -> R is Lebesgue measurable on R-2 and Lambda is a non-empty set of indices. Further, we provide an example to support these theoretical results.