On Fatou type convergence of higher derivatives of certain nonlinear singular integral operators


  • Harun Karsli Abant Izzet Baysal University
  • H. Erhan Altin Abant Izzet Baysal University


nonlinear singular integral operator, pointwise convergence, Fatou type convergence


The present paper concerns with the Fatou type convergence properties of the \(r-th\) and \((r+1)-th\) derivatives of the nonlinear singular integral operators defined as \[ \left( I_{\lambda}f\right) (x)=\int\limits_{a}^{b}K_{\lambda}(t-x,f(t))\,{\rm d}t,\,\,\,\,\,\,\,x\in\left( a,b\right) , \] acting on functions defined on an arbitrary interval \(\left( a,b\right) ,\) where the kernel \(K_{\lambda}\) satisfies some suitable assumptions. The present study is a continuation and extension of the results established in the paper [7].


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How to Cite

Karsli, H., & Altin, H. E. (2013). On Fatou type convergence of higher derivatives of certain nonlinear singular integral operators. Rev. Anal. Numér. Théor. Approx., 42(1), 37–48. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2013-vol42-no1-art3