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Öğe On approximation properties of certain multidimensional nonlinear integrals(Int Scientific Research Publications, 2016) Almali, Sevgi Esen; Gadjiev, Akif D.We prove theorems on convergence of multidimensional nonlinear integrals in Lebesgue points of generated function, and show that the main results are applicable to a wide class of exponentially nonlinear integral operators, which may be constructed by using well known positive kernels in approximation theory. (C) 2016 All rights reserved.Öğe On pointwise convergence of the family of Urysohn-type integral operators(Wiley, 2019) Almali, Sevgi EsenIn this paper, we consider a family of nonlinear integral operators of Urysohn-type and study the pointwise convergence of the family at characteristic points of L-1-function. The kernel K-lambda(x, t, u(t)) depends on the positive parameter lambda changing on the set of numbers with the accumulation point at infinity and K-lambda(x, t, u(t)) is an entire analytic function of variable u, which is a bounded function belonging to L-1(R).Öğe On Singular Integral Operators Involving Power Nonlinearity(Kangwon-Kyungki Mathematical Soc, 2017) Almali, Sevgi Esen; Uysal, Gumrah; Mishra, Vishnu Narayan; Guller, Ozge OzalpIn 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)