99. Yongping Liu,
Chunmei Su, V.I. Ivanov,
Some Problems of
Approximation Theory in the Spaces
98. Song Chunyuan, Liu Yongping, The optimal recovering problem of Lipschitz functions of α order, J. Beijing Normal University(Natural Science), 46:5(2010), 565-568 (in Chinese).
97. Liu Yongping, Yang Wei, Relative n-widths of the classes of differentiable functions and the periodic converlution classes in Lq metric, Acta Mathematica Sinica, Chineses Serie, 53:6(2010), 1087-1096. (in Chinese)
96. Yang Zhuyuan, Yang Zongwen, Liu Yongping, Average onesided widths of Sobolev and Besov classes, Acta Mathematica Scientia, Series B, Vol. 30:1(2010), 147-160.
95. Li Rensuo, Liu Yongping, Best m-term one-sided trigonometric approximation of some function classes defined by a kind of multipliers, Acta Mathematica Sinica, English Series, Vol. 26：5(2010)，975-984.
94. Liu Yongping, Xiao Weiwei, Yang Wei, The research progress of BNU group on relative widths, International Journal of Wavelets, Multiresolution and Information Processing (IJWMIP),7:6(2009), 803-811.
93. Xiao Weiwei, Liu Yongping, Relative widths of function classes of L_2(T) determined by fractional order derivatives in L_q(T), Acta Math. Scientia, 29A:4, (2009), 833-842. (in Chinese)
92. Li Jian, Liu
Yongping,
Relationship of two classes of
functions defined on a plane, Beijing Normal
University(Natural Science), 44:6(2008), 573-576 (in Chinese).
91. Yang Wei, Liu Yongping, Relative n-widths of periodic convolution classes with NCVD-kenel and B-kenel, Science in China, Series A, 39:6(2009), 700-708 (in Chinese); Science China: Mathematics, 53:1(2010), 165-172(in English).
90. Yang Lianhong, Liu Yongping, Relative widths of smooth functions determined by linear differential operator, J. Math. Anal. Appl., 351:2(2009), 734-746. pdf
89. Yang Wei, Liu Yongping, Relative width of the classes of differentiable functions and the periodic convolution class in L_1 metric, J. Beijing Normal University(Natural Science), 44:6(2008), 573-576 (in Chinese).
88. Li Jian, Liu Yongping, The Jackson inequality for the best L^2-Approximation of functions on [0, 1] with the weight x, Numerical Mathematics:Theory, Methods and Applications, 1:3(2008), 340-356. pdf
87. Li Rensuo, Liu Yongping, the Asymptotic estimations of best m-term one-side approximation of function classes determined by Fourier series, Advance in Mathematics (CHINA), 37:2(2008), 211-221.
86. Liu Yongping, Xiao Weiwei, Relative Average widths of Sobolev spaces in L_2(R^d), Analysis Mathematica, 34(2008), 71-82. pdf
85. Liu Yongping, Yang Lianhong, Relative widths of smooth functions determined by fractional order
derivatives, J. Complexity, 24:2(2008), 259-282. pdf
84. Ivanov, V. I.; Chertova, D. V.; Liu, Yong Ping, The Jackson theorem in the space $L\sb 2$ on the interval [-1,1] with a power weight. Mat. Zametki, 84 :1(2008), 136--138 (for brief in Russian); Trudy Institua Matematiki i Mekhaniki UrO RAN, 14:2(2008 ), (for whole-length in Russian); Proceedings of the Steklov Institute of Mathematics, 2008, suppl. 2 (for whole-length in English).
83. Li Rensuo, Liu Yongping, Asymptotic estimations of m-term approximation and greedy algorithm for multiplier function classes defined by Fourier series, Chinese J. Engineer Mathematics, 25:1(2008), 89-96.(in Chinese)
82. Xiao Wewei, Liu Yongping, Relative width of classes of differentiable functions in the L_2 metric, J. Beijing Normal University(Natural Science), 43:5(2007), 493-495. (in Chinese)
81. Geng Aicheng, Liu Yongping, Kolmogorov n-width of some special classes of functions in L_2, J. Beijing Normal University(Natural Science), 43:5(2007), 496-500.(in Chinese)
80. Yang, Zhuyuan; Yang, Zongwen; Liu, Yongping, Onesided widths of periodic Besov classes. Southeast Asian Bull. Math. 31:2 (2007), 387-394.
79. Yang Zhuyuan, Yang Zongwen, Liu Yongping, Average one-sided widths of anisotropic Sobolev and Besov classes, Acta Mathematca Sinica, Chinese Series, 50:5(2007), 1177-1184.
78. Gui Shaohui, Liu Yongping, Asymptotic estimate for the Lebesgue constant of cardinal L- spline interpolation operator, East Journal on Approximation, 3(2007), 331-355.
77. Hui Cao, Yongping Liu. Lebesgue constants on Gaussian cardinal interpolation operators from l(Z) into L(R). Analysis Mathematica, 32(2006), 265-277.
76. Liu Yongping, Yang Lianhong, Relative width of smooth classes of multivariate periodic functions with restrictions on iterated Laplace derivatives in the L_2-metric, Acta Math. Scientia, 26B:4, (2006), 720-728.
75. Gui Qiao XU, Yong Sheng SUN, Yong Ping LIU. N- widths and average widths of Besov classes in Sobolev spaces, Acta Math. Sinica, English Series, 22:6 (2006), 1667-1678.
74. Yang Zhuyuan, Liu Yongping, Approximation by cardinal Hermite splines, J. Yunan University(Natural Science), 28:5(2006), 374-377.
73. Yang Zhuyuan, Liu Yongping, Approximation of Lipschitz spaces from cardinal splines, J. Yunan University(Natural Science), 28:4(2006), 281-284.
72. Yang Zhuyuan, Liu Yongping, Approximation of Multivariate Cardinal Splines, J. Beijing Normal University(Natural Science), 42:3(2006), 221-223.
71. Gui Shaohui, Liu Yongping, Strong asymptotic estimate for Lebesgue constant on Gaussian cardinal interpolation operator, J. Beijing Normal University(Natural Science), 42:2(2006), 116-119.
70. Hu Yingkang, Liu Yongping, On equivalence of moduli of smoothness of polynomials in $L\sb p$, $0<p \leq \infty$. J. Approx. Theory, 136:2(2005), 182--197.
69. Zhou Heng, Liu Yongping, Shi Limin, On the convergence of a positive linear operator sequences, J. Beijing Normal University(Natural Science), 41:4(2005), 346-347.
68. Li Rensuo, Liu Yongping, Asymptotic estimate of m-term approximation and greedy algorithm of the classes defined by a multiplier, J. Beijing Normal University(Natural Science), 41:2(2005), 127-130.
67. Yang Lianhong, Liu Yongping, Relative widths of classes of multivariate differentiable functions in the space L_2(R^d), J. Beijing Normal University(Natural Science), 41:1(2005), 21-23.
66. Ren Meiying, Liu Yongping. A 2-periodic entire (m_1,m_2; m'_1, m'_2) interpolation problem on equidistant nodes, Journal of Tianjin Normal University(Natural Science), 24:3 (2004), 37-41.
65. Yongping Liu; Guiqiao Xu. Infinite-dimensional Gel'fand \sigma widths of anisotropic Besov classes, PanAmerican Mathematical Journal, 14:3(2004), 65-77.
64. Xu, Guiqiao; Liu, Yongping. The average widths of Sobolev-Wiener classes and Besov-Wiener classes, Acta Math. Sinica, English Series, 20:1 (2004), 81-92.
63. Liu, Yongping; Xu, Guiqiao. Widths and average widths of Sobolev classes. Acta Math. Scientia, 23B:2, (2003), 178-184. SCI
62. Liu, Yongping; Xu, Guiqiao. The Average widths and non-linear widths of the classes of multivariate functions with bounded moduli of smoothness. Acta Math. Applicatae Scientia (English Series), 18:4, (2002), 663-674.
61. Xu, Guiqiao; Liu, Yongping. The Gel' fand widths of anisotropic Sobolev classes of smooth functions. Anal. Math. 28 (2002), no. 4, 317--332.
60. Liu, Yongping; Xu, Guiqiao. The infinite-dimensional widths and optimal recovery of generalized Besov classes. J. Complexity 18 (2002), no. 3, 815--832. SCI
59. Liu, Yongping; Lu, Guozhen;
Wheeden, Richard L.. Some equivalent definitions of high order
Sobolev spaces on stratified groups and generalizations to metric spaces.
Math. Ann. 323 (2002), no. 1, 157--174. SCI
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