Approximation of a class of non-linear integral operators / Non-lineer İntegral Operatörlerin Bir Sınıfının Yaklaşımı

Abstract

In this study,we investigate the problem of pointwise convergence at lebesgue points of f funtions for the family of non-linear integral operators

                                                      

where  is a real parameter,  is non-negative kernels and  is the function in . We consider two cases where  is a finite interval and when is the whole real axis.

Keywords

• Approximation,nonlinear integral operators,lebesque point

References

1. 1] Muscielek, J. Approximation by Nonlinear Singular Integral Operators In Generalized Orlicz Spaces, Comment. Math., 1991; 31, 79-88.
2. [2] widerski, T.; Wachnicki, E. Nonlinear Singular Integral Depending On Two Parameters, Comment. Math. Prace Mat. 2000; 40, 181–189.
3. [3] Karsli,H. Convergence and Rate of Convergence by Nonlinear Singular Integral Operators Depending on Two Parameters, Appliable Analysis, 2010; 85 (6-7), 781-791.
4. [4] Karsli, H.; Gupta, V. Rate of Convergence of Nonlinear Integral Operators for Functions of Bounded Variation. Calcolo 2008; 45 (2), 87–98.
5. [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. [6] Bardora, C.; Vinti, G.; Karsli,H. Nonlinear Integral Operators with Homogeneous Kernels: Pointwise Approximation Theorems, Applicable Analysis, 2011; 90 (3-4), 463-474.
7. [7] Karsli, H. On Approximation Properties of Non-convolution Type Nonlinear Integral Operators.Anal. Theory Appl. 2010; 26 (2), 140–152.
8. [8] Almali,S. E. and Gadjiev,G.D. On Approximation Properties of Certain Multidimensional Nonlinear Integrals. J. Nonlinear Sci. Appl. 2016; 9 (5), 3090–3097.

9. [9] Bardora, C.; Musceilak, J.; 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. [10] Butzer, P.L.; Nessel, R.J. Fourier Analysis and Approximation, Vol. 1, Academic Press, New York,London, 1971.