Approximation of Class of Non-linear Integral Operators

Approximation of Class of Non-linear Integral Operators

In this study,we investigate the problem of pointwise convergence at lebesgue points of funtions forthe family of non-linear integral operatorsL,(f,x) f’”(t)Km(x,t)dtmilwhere fl, is real parameter, (x, t) is non-negative kernels and is the function in L1(a, b)We consider two cases where (a b) is finite interval and when is the whole real axis.

___

  • [1] Musielek, ]. Approximation by Nonlinear Singular Integral Operators In Generalized Orlicz Spaces, Comment. Math., 1991; 31, 79-88.
  • [2] S’widerski, T.; Wachnicki, E. Nonlinear Singular Integral Depending On Two Parameters, Comment. Math. Prace Mat. 2000; 40, 181—189.
  • [3] Karsli,H. Convergence and Rate of Convergence by 411 CBU ]. of Sci., Volume 13, Issue 2, 407-411
  • Nonlinear Singular Integral Operators Depending on Two Parameters, Appliable Analysis, 2010; 85 (6-7), 781—791.
  • [4] Karsli, H.; Gupta, V. Rate of Convergence of Nonlinear Integral Operators for Functions of Bounded Variation. Calcolo 2008; 45 (2), 87—98.
  • [5] Angeloni, L.; Vinti, G.Convergence in Variation and Rate of Approximation for Nonlinear Integral Operators of Convolution Type, Results in Mathematics, 2006; 49, 1- 23.
  • [6] Bardaro, C.; Vinti, G.; Karsli,H. Nonlinear Integral Operators with Homogeneous Kernels: Pointwise Approximation Theorems, Applicable Analysis, 2011; 90 (3-4), 463-474.
  • [7] Karsli, H. On Approximation Properties of Nonconvolution Type Nonlinear Integral Operators.Anal. Theory Appl. 2010; 26 (2), 140—152.
  • [8] A1ma1i,S. E. and Gadjiev,G.D. On Approximation Properties of Certain Multidimensional Nonlinear Integrals. ]. Nonlinear Sci. Appl. 2016; (5), 3090—3097.
  • [9] Bardaro, C.; Musielak, ].; Vinti, G. Nonlinear Integral Operators and Applications. De Grayter Series in Nonlinear Analysis and Applications, Walter de Gruyter Co., Berlin, 2003; 9, xii+201.
  • [10] Butzer, P.L.; Nessel, R.]. Fourier Analysis and Approximation, Vol. 1, Academic Press, New York,London, 1971.