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Yongping Liu, Guiqiao Xu. Two results om (s,t)-weak tractability of linear tensor product problems in the average case setting, Numerical Mathematics: A Journal of Chinese university, 41:1(2019),80-87.
Guiqiao Xu, Yongping Liu, Jie Zhang. Weighted integral of infinitely differentiable multivariate functions is exponentially convergent, Numerical Mathematics: Numerical Mathematics: Theory, Methods and Applications, 12:1(2019),98-114.
Guiqiao Xu, Yongping Liu, Liyan Xiong. Exact Constants for Simultaneous Approximation of Sobolev Classes by Piecewise Hermite Interpolation, Analysis Mathematica, to have been aceepted.
Yongping Liu, Guiqiao Xu. (s,t)-weak tractability of multivariate linear problems in the average case setting, Acta Mathematica Scientia, 39B(4)(2019), 1033-1052.
Yongping Liu, Guiqiao Xu, Jie Zhang. Best restricted approximation of smooth function classes, Trudy Inst. Mat. i Mekh. UrO RAN, 24:4 (2018), 283–294
Yi Gu, Yongping Liu. Optimal recovery of multivariate functions restricted by second-order differential operator, Analysis and Applications, Volume 16, Issue 04(July 2018), 585-599.
Yongping Liu, Guiqiao Xu，Jie Zhang. Exponential Convergence of an Approximation Problem for Infinitely Differentiable Multivariate Functions, Mathematical Notes, Vol.103(5-6): 769–779. June 2018.
Liu Yongping, Xu Guiqiao. Exponential convergence (s,t)-weak tractability of general multivariate linear problems, Journal of Beijing Normal University, Nature Science, (in Chinese), 53(6):631-634, 2017.
Yongping Liu, Guiqiao Xu. Average case tractability of a multivariate approximation problem, Journal of Complexity, Volume 43, Pages 76-102, December 2017.
Bo Ling, Yongping Liu. Best restriction approximation by entire functions of exponential type (in Chinese), Acta Mathematica Sinica, Chinese Series, 60:3(2017), 389-400. May 2017.
Yongping Liu, Guiqiao Xu. EC-tractability of general multivariate linear problems, Numerical Mathematics, A Journal of Chinese Universities, (in Chinese),Volume 38:4, Pages 375-384, December 2016.
Yongping Liu, Guiqiao Xu. A note on tractability of multivariate analytic problems, Journal of Complexity, Volume 34, Page 42-49, 2016.
Liu Yongping, Wu Wenyan, Xu Guiqiao. The best constants in the Wirtinger inequality, International Journal of Wavelets, Multiresolution and Information Processing, Vol. 14 (2016), No. 06, 1650048, pp13. November 2016.
Chen Hanping, Liu Yongping, Xu Guiqiao. The Smolyak algorithm based on cardinal spline interpolation, Journal of Beijing Normal University, Nature Science, (in Chinese), 52(1):1-4, 2016.
Liu Yongping, Xu Guiqiao. A note on tractability of multivariate analytic problems, Journal of Complexity 34, 42–49, 2016.
Dai Guangxin, Liu Yongping, Xu Guiqiao. Two sharp approximation inequalities, Journal of Beijing Normal University, Nature Science, (in Chinese), 51(5):455-458, 2015.
Liu Yongping, Xu Guiqiao. L^κ-weak tractability of general multivariate problems in the average case setting, Journal of Beijing Normal University, Nature Science, (in Chinese), 51(4): 354-357, 2015.
Gu Yi, Liu Yongping. The sharp Jackson inequality for L^2-approximation on the periodic cylinder. Acta Mathematica Scientia, 35B(2): 375-382, 2015.
Gu Yi, Liu Yongping. The sharp Jackson inequality for L^2-approximation on the cylinder (in Chinese). Numerical Mathematics, A Journal of Chinese Universities, 36(2): 360-369, 2014.
Liu Yongping, Song Chunyuan. Dunkl's theory and Best approximation by entire functions of exponential type in L2-metric with power weight, Acta Mathematica Sinica, English Series, 30:10(2014), 1748-1762.
Liu Yongping. Higher monotonicity properties of nomalized Bessel functions, International Journal of Wavelets, International Journal of Wavelets, Multiresolution and Information Processing, 12:5 (2014) .
Huang Rong, Liu Yongping. Best restriction L1-approximation of periodic convolution class by generalized splines, International Journal of Wavelets, Multiresolution and Information Processing, 12:5 (2014) .
Ling Bo, Liu Yongping. Optimal recovery of isotropic classes of rth dierentiable functions on Rd, Numerical Functional Analysis and Optimization, 35:6(2014), 724-738.
Ling Bo, Liu Yongping. Optimal recovery of isotropic classes of rth differntiable multivariate functions, BIT Numer Math, 54:2(2014), 485-500.
Ling Bo, Liu Yongping. Optimal recovery of isotropic classes of twice-differentiable functions defined on d-dimensional Euclidean space, J. Approximation Theory, 182: 83-91, 2014.
Gu Yi, Liu Yongping. The sharp constants in the Jackson inequality in weighted L^2(B^d). Journal of Beijing Normal University, Nature Science, (in Chinese), 49(4): 347-350, 2013.
Ling Bo, Liu Yongping, Best constants of harmonic approximation of some convolution classes associated with Laplace operator in d-variables, SCIENCE CHINA, Mathematics, Vol. 56 No. 2: 301–313, 2013.
Ling Bo, Liu Yongping, Birkhoff Interpolation of Cardinal Splines, Sciencepaper Online, http://www.paper.edu.cn/releasepaper/content/201212-162.html. .
Sun Huan, Liu Yongping, Sharp Jackson inequality in weighted L2-space of half real axis with generalized Laguerre weight (in Chinese), Highlights of Sciencepaper Online, 2013，6(1)：8-15. (in Chinese)
Jian Li, Yongping Liu, Chunmei Su, The Jackson inequality and widths of function classes in L2([0, 1], x2v+1), Journal of Complexity 28 (2012), 582–596.
Li Rensuo, Liu Yongping, The Best m-Term One-Sided Approximation of Besov Classes by the Trigonometric Polynomials, Advances in Pure Mathematics, 2012, 2, 183-189
V.I. Ivanov, Yongping Liu, O. I. Smirnov, Some inequalities for entire functions of exponential type in Lp(Rd)-spaces with power weight, Proceedings of Tula State University. Natural sciences. 2011. Iss.2. 70-80.
V.I. Ivanov,Yongping Liu, Lower estimation of Jackson constants in Lp-spaces with periodical Jacobi weight, Proceedings of Tula State University. Natural Sciences. 2011. Iss.2., 59-70.
Yongping Liu, Chunmei Su, V.I. Ivanov, Some Problems of Approximation Theory in the Spaces L_p on the Line with Power Weight, Mat. Zametki, 90:3 (2011), 362–383.
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).
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)
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.
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.
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.
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)
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).
Yang Lianhong, Liu Yongping, Relative widths of smooth functions determined by linear differential operator, J. Math. Anal. Appl., 351:2(2009), 734-746. pdf
Li Jian, Liu Yongping, Relationship of two classes of functions defined on a plane, Beijing Normal University(Natural Science), 45:3(2009), 226-231 (in Chinese).
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).
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
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.
Liu Yongping, Xiao Weiwei, Relative Average widths of Sobolev spaces in L_2(R^d), Analysis Mathematica, 34(2008), 71-82. pdf
Liu Yongping, Yang Lianhong, Relative widths of smooth functions determined by fractional order derivatives, J. Complexity, 24:2(2008), 259-282. pdf
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).
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)
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)
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)
Yang, Zhuyuan; Yang, Zongwen; Liu, Yongping, Onesided widths of periodic Besov classes. Southeast Asian Bull. Math. 31:2 (2007), 387-394.
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.
Gui Shaohui, Liu Yongping, Asymptotic estimate for the Lebesgue constant of cardinal L- spline interpolation operator, East Journal on Approximation, 3(2007), 331-355.
Hui Cao, Yongping Liu. Lebesgue constants on Gaussian cardinal interpolation operators from l(Z) into L(R). Analysis Mathematica, 32(2006), 265-277.
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.
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.
Yang Zhuyuan, Liu Yongping, Approximation by cardinal Hermite splines, J. Yunan University(Natural Science), 28:5(2006), 374-377.
Yang Zhuyuan, Liu Yongping, Approximation of Lipschitz spaces from cardinal splines, J. Yunan University(Natural Science), 28:4(2006), 281-284.
Yang Zhuyuan, Liu Yongping, Approximation of Multivariate Cardinal Splines, J. Beijing Normal University(Natural Science), 42:3(2006), 221-223.
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.
Hu Yingkang, Liu Yongping, On equivalence of moduli of smoothness of polynomials in $L\sb p$, $0
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