Relative Widths of Some Sets of l^{m}_{p}

References

[1] V. N. Konovalov, “Estimates of Diameters of Kolmogorov Type for Classes of Differentiable Periodic Functions,” Mate-maticheskie Zametki, Vol. 35, No. 3, 1984, pp. 369-380.

[2] V. F. Babenko, “On the Relative Widths of Classes of Functions with Bounded Mixed Derivative,” East Journal on Approximations, Vol. 2, No. 3, 1996, pp. 319-330.

[3] V. F. Babenko, “Approximation in the Mean under Restriction on the Derivatives of the Approximating Functions, Questions in Analysis and Approximations,” Insti-tute of the Mathematics of the Ukrainean Academy of Science, Kiev, 1989, pp. 9-18. (in Russian)

[4] V. F. Babenko, “On Best Uniform Approximations by Splines in the Presence of Restrictions on Their Derivatives,” Mathematical Notes, Vol. 50, No. 6, 1991, pp. 1227-1232. Translated from Mate-maticheskie Zametki, Vol. 50, No. 6, 1991, pp. 24-30.

[5] V. N. Konovalov, “Approximation of Sobolev Classes by Their Sections of Finite Dimensional,” Ukrainian Mathematical Journal, Vol. 54, No. 5, 2002, pp. 795-805.
doi:10.1023/A:1021635530578

[6] V. N. Konovalov, “Ap-proximation of Sobolev Classes by Their Finite-Dimensional Sections,” Matematicheskie Za- metki, Vol. 72, No. 3, 2002, pp. 370-382.

[7] Y. N. Subbotin and S. A. Telyakovskii, “Exact Values of Relative Widths of Classes of Differentiable Func-tions,” Mathematical Notes, Vol. 65, No. 6, 1999, pp. 731-738. Translated from Matematicheskie Zametki, Vol. 65, No. 6, 1999, pp. 871-879.

[8] Y. N. Subbotin and S. A. Telyakovskii, “Relative Widths of Classes of Differentiable Functions in the Metric,” Russian Mathematical Surveys, Vol. 56, No. 4, 2001, pp. 159-160.

[9] Y. N. Subbotin and S. A. Telyakovskii, “On Relative Widths of Classes of Differentiable Functions,” Proceedings of the Steklov Institute of Mathematics, 2005, pp. 243-254.

[10] V. T. Shevaldin, “Approximation by Local Trigonometric Splines,” Mathematical Notes, Vol. 77, No. 3, 2005, pp. 326-334.

[11] V. M. Tikhomirov, “Some Remarks on Relative Diameters,” Banach Center Publications, Vol. 22, 1989, pp. 471-474.

[12] W. W. Xiao, “Relative Widths of Classes of Functions Defined by a Self-Conjugate Linear Dif-ferential Operator in (in Chinese),” Chinese annals of Mathematics, Vol. 29A, No. 5, 2008, pp. 679-688.

[13] W. W. Xiao, “Relative Infinite-Dimensional Width of Sobolev Classes,” Journal of Mathematical Analysis and Applications, Vol. 369, No. 2, 2010, pp. 575-582.
doi:10.1016/j.jmaa.2010.03.050

[14] Y. P. Liu and W. W. Xiao, “Relative Average Widths of Sobolev Spaces in ,” Analysis Mathematica, Vol. 34, No. 1, 2008, pp. 71-82.
doi:10.1007/s10476-008-0107-8

[15] Y. P. Liu and L. H. Yang, “Relative Width of Smooth Classes of Multivariate Periodic Functions with Restrictions on Interated Laplace Derivatives in The -Met- Ric,” Acta Mathematica Scientia, Vol. 26B, No. 4, 2006, pp. 720-728.
doi:10.1016/S0252-9602(06)60098-2

[16] Y. P. Liu and L. H. Yang, “Relative Widths of Smooth Factions Determined by Fractional Order Derivatives,” Journal of complexity, Vol. 24, No. 2, 2008, pp. 259-282.

[17] L. H. Yang and Y. P. Liu, “Relative Widths of Smooth Functions Determined by Linear Differential Operator,” Journal of Mathematical Analysis and Applications, Vol. 351, No. 2, 2009, pp. 734-746.
doi:10.1016/j.jmaa.2008.11.009

[18] G. G. Lorentz, M. V. Golitschek, and Y. Makovoz, “Constructive Approximation,” Springer, Berlin, 1996.

[19] A. Pinkus, “N-Widths in Ap-proximation Theory,” Springer, Berlin, 1985.