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In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power nonlinearity given in the following form: \begin{equation*} T_{\lambda }(f;x)=\int \limits_{a}^{b}\sum \limits_{m=1}^{n}f^{m}(t)K_{\lambda ,m}(x,t)dt,\text{ }\lambda \in \Lambda ,\text{ }x\in \left( a,b\right) , \end{equation*} where $\Lambda $ is an index set consisting of the non-negative real numbers, and $n\geq 1$ is a finite natural number, at $\mu -$generalized Lebesgue points of integrable function $f$ $\in L_{1}\left( a,b\right) .$ Here, $f^{m}$ denotes $m-th$ power of the function $f$ and $\left( a,b\right)$ stands for arbitrary bounded interval in $ \mathbb{R} $ or $\mathbb{R}$ itself. We also handled the indicated problem under the assumption $f$ $\in L_{1}\left( \mathbb{R}\right) .$
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참고문헌 (19)
참고문헌 신청
A. D. Gadjiev / 1966 / On nearness to zero of a family of nonlinear integral operators of Hammerstein, Izv. Akad. Nauk Azerbadzan / SSR Ser. Fiz.-Tehn. Mat. Nauk 2 : 32 ~ 34
A. D. Gadjiev / 1968 / The order of convergence of singular integrals which depend on two parameters, Special Problems of Functional Analysis and their Appl. to the Theory of Diff. Eq.
B. Rydzewska / 1973 / Approximation des fonctions par des int e grales singuli eres ordi-naires / Fasc. Math 7 : 71 ~ 81
C. Bardaro / 1984 / On approximation properties for some classes of linear operators of convolution type / Atti Sem. Mat. Fis. Univ. Modena 33 (2) : 329 ~ 356
C. Bardaro / 1990 / On approximation properties of certain nonconvolution integral operators / J. Approx. Theory 62 (3) : 358 ~ 371
A. D. Gadjiev / 1968 / The order of convergence of singular integrals which depend on two parameters, Special Problems of Functional Analysis and their Appl. to the Theory of Diff. Eq.
B. Rydzewska / 1973 / Approximation des fonctions par des int e grales singuli eres ordi-naires / Fasc. Math 7 : 71 ~ 81
C. Bardaro / 1984 / On approximation properties for some classes of linear operators of convolution type / Atti Sem. Mat. Fis. Univ. Modena 33 (2) : 329 ~ 356
C. Bardaro / 1990 / On approximation properties of certain nonconvolution integral operators / J. Approx. Theory 62 (3) : 358 ~ 371
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