On convergence of nonlinear singular integral operators with non-isotropic kernels
Keywords:
Nonlinear singular integral, non-isotropic distance, Lipschitz condition.Abstract
Here we give some approximation theorems concerning pointwise con- vergence and rate of pointwise convergence of nonlinear singular integral opera- tors with non-isotropic kernels of the form ...
Mathematics Subject Classifification (2010): 41A35, 41A25, 47G10.
References
Anastassiou, G.A., Aral, A., Generalized Picard singular integrals, Comput. Math. Appl., 57(2009), no. 5, 821-830.
Aral, A., On convergence of singular integrals with non-isotropic kernels, Commun. Fac. Sci. Univ. Ank. Ser. A1, 50(2001), 88-98.
Aral, A., The Convergence of singular integrals, (in Turkish), Ph.D. Thesis, Ankara University, 2001, 50 pages.
Bardaro, C., Musielak, J., Vinti, G., Nonlinear integral operators and applications, De Gruyter Series in Nonlinear Analysis and Applications, 9(2003), xii + 201 pp.
Bardaro, C., Musielak, J., Vinti, G., Modular estimates and modular convergence for a class of nonlinear operators, Math. Japonica, 39(1994), no. 1, 7-14.
Bardaro, C., Musielak, J., Vinti, G., Approximation by nonlinear singular integral operators in some modular function spaces, Annales Polonici Mathematici, 63(1996), no. 2, 173-182.
Besov, O.V., Nikolsky, S.M., IIin, V.P., The Integral Representation of Functions and Embedding Theorems, (in Russian), Nauka, 1975.
I.Cinar, The Hardy-Littlewood-Sobolev inequality for non-isotropic Riesz potentials, Turkish J. Math., 21(1997), no. 2, 153-157.
Karsli, H., On approximation properties of a class of convolution type nonlinear singular integral operators, Georgian Math. J., 15(2008), no. 1, 77{86.
Karsli, H., Gupta, V., Rate of convergence by nonlinear integral operators for functions of bounded variation, Calcolo, 45(2008), no. 2, 87-99.
Karsli, H., Ibikli, E., On convergence of convolution type singular integral operators depending on two parameters, Fasciculi Mathematici, 38(2007), 25-39.
Musielak, J., On some approximation problems in modular spaces, In Constructive Function Theory 1981, (Proc. Int. Conf., Varna, June 1-5, 1981), Publ. House Bulgarian Acad. Sci., Sofia 1983, 455-461.
Neri, U., Singular Integrals, Springer-Verlag, 1971.
Sarikaya, M.Z., Yildirim, H., On the β spherical Riesz potential generated by the β distance, Int. J. Contemp. Math. Sci., 1(2006), no. 1-4, 85-89.
Swiderski, T., Wachnicki, E., Nonlinear singular integrals depending on two parameters, Commentationes Math., 40(2000), 181{189.
Yilmaz, B., Some approximation properties of generalized Picard operators, (in Turkish), Ph.D. Thesis, Ankara University, 2012, 56 pages.
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