A Note On Convergence of Nonlinear General Type Two Dimensional Singular Integral Operators

Abstract

Keywords

• Lebesgue point,nonlinear singular integral,Lipschitz condition

References

1. [1] J. Musielak, “On some approximation problems in modular spaces”, In: Constructive Function Theory, Proceedings of InternationalConference Varna, 1-5 June, 1981, Publication House of Bulgarian Academic of Sciences, Sofia, pp. 181-189, 1983.
2. [2] C. Bardaro, H. Karsli and G. Vinti, “On pointwise convergence of linear integral operators with homogeneous kernels”, Integral Transforms and Special Functions, 19(6), (2008), 429–439.
3. [3] C. Bardaro, H. Karsli and G. Vinti, “Nonlinear integral operators with homogeneous kernels: pointwise approximation theorems”, Appl. Anal., Vol. 90, Nos. 3–4, 463–47, 2011
4. [4] H. Karsli, “Convergence and rate of convergence by nonlinear singular integral operators on two parameters”, Appl. Anal., 85, 781-791, 2006.
5. [5] T. Swiderski and E. Wachnicki, “Nonlinear singular integrals depending on two parameters”, Comment. Math., 40, pp. 181-189, 2000.
6. [6] J. Musielak, “Approximation by nonlinear singular integral operators in generalized Orlicz spaces”, Comment. Math. Prace Mat., 31, pp. 79—88, 1991.
7. [7] C. Bardaro and G. Vinti, “Approximation by nonlinear integral operators in some modular function spaces, Ann. Polon. Math., 63, pp.173-182, 1996.
8. [8] C. Bardaro, J. Musielak, and G. Vinti, “Nonlinear integral operators and applications”, De Gruyter Series in Nonlinear Analysis and Applications, Vol. 9, Walter de Gruyter, Publ., Berlin-New York, 2003.

9. [9] C. Bardaro and I. Mantellini, “Pointwise convergence theorems for nonlinear Mellin convolution operators”, Int.J.Pure Appl. Math., 27(4), 431-447, 2006.
10. [10] C. Bardaro, G. Vinti and H. Karslı, “On pointwise convergence of linear integral operators with homogeneous kernels”, Integral Transform Sec. Funct., 19(6), pp. 429-439, 2008.
11. [11] H. Karsli, “On approximation properties of non-convolution type nonlinear operators”, Anal. Theory Appl. 26 (2), 140-152, 2010.
12. [12] G. Uysal, M. Menekse Yilmaz and E. Ibikli, “On pointwise convergence of bivariate nonlinear singular integral operators”, Kuwait Journal of Science, 44(2):46-57, 2017.
13. [13] B. Rydzewska, “Approximation des fonctions de deux variables par des integrales singulieres doubles”, Fasc. Math., 8, pp. 35--45 (in French), 1974.
14. [14] S. Esen Almali, “On approximation properties of certain multidimensional nonlinear integrals”, Journal of NonlinearSciences and Applications, (9)5, 3090-3097, 2016.
15. [15] P. L. Butzer and R. J., Nessel, Fourier Analysis and Approximation, Academic Press, New York, London, 1971.
16. [16] M. Yilmaz Menekse,. “A study on convergence of nonconvolution type double singular integral operators”, New Trends Math. Sci., 4 (4) 67-78, 2016.
17. [17] R. Taberski, “On double integrals and Fourier Series” Ann. Polon. Math. 15, pp. 97-115, 1964.