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| 1 | Ultimate generalization to monotonicity for uniform convergence of trigonometric series显示文摘Chaundy and Jolliffe proved that if {a n } is a non-increasing (monotonic) real sequence with lim n →∞ a n = 0, then a necessary and sufficient condition for the uniform convergence of the series ∑∞ n=1 a n sin nx is lim n →∞ na n = 0. We generalize (or weaken) the monotonic condition on the coefficient sequence {a n } in this classical result to the so-called mean value bounded variation condition and prove that the generalized condition cannot be weakened further. We also establish an analogue to the generalized Chaundy-Jolliffe theorem in the complex space. | Zhou SongPing Zhou Ping Yu DanSheng | 2010 | Science China Mathematics2010，53，7： | 9 |
| 2 | Weighted approximation by Bernstein quasiinterpolants for functions with singularities显示文摘 | Yi ZHAO Dansheng YU | 2013 | Frontiers of Mathematics in China2013，8，6： | 2 |
| 3 | On Weighted L^p-Approximation by Weighted Bernstein-Durrmeyer Operators显示文摘In the present paper,we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted L^p-norm with Jacobi weight w(x) = x~α(1-x)~β.All the results involved have no restriction α,β < 1-1/p,which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators. | Meiling Wang Dansheng Yu Dejun Zhao | 2018 | Analysis in Theory and Applications2018，34，1： | 2 |
| 4 | On the degree of approximation of continuous functions by means of fouries series显示文摘 | Wei Baorong Yu Dansheng | 2012 | Math Commnun2012，17，： | 1 |
| 5 | ON WEIGHTED L^p INTEGRABILITY AND APPROXIMATION OF TRIGONOMETRIC SERIES显示文摘We generalize several classical results on the integrability of trigonometric series and relations among the best approximation and the coefficients of trigonometric series. Theorem 3 and Theorem 4 are the first results on the relations among the weighted best approximation and the coefficients of trigonometric series. | Baorong Wei and Dansheng Yu Department of Mathematics Hangzhou Normal University Hangzhou, 310036P. R. China Department of Mathematics Hangzhou Normal University Hangzhou, 310036 P. R. China and Department of Mathematics Statistics and Computer Sciences St Franics Xaiver University Antigonish, Nova ScotiaCanada B2G 2w5 | 2009 | Analysis in Theory and Applications2009，25，1： | 1 |
| 6 | An application of generalized power increasing sequences on factors theorem显示文摘 | Bor H Yu Dansheng | 2013 | Bull Belg Math Soc Simon Stevin2013，20，： | 1 |
| 7 | On ap- proximation by Bernstein-Stancu type operator显示文摘 | WANG Meiling YU Dansheng ZHOU Ping | 2014 | Ap- pl Math Comput2014，246，1： | 1 |
| 8 | Global and point- wise estimates for approximation by rational functions with polynomials of positive coefficients as the denom- inators显示文摘 | YU Dansheng ZHOU Songping | 2011 | Acta Math Sci2011，31，2： | 1 |
| 9 | APPROXIMATION BY RATIONAL FUNCTIONS WITH POLYNOMIALS OF POSITIVE COEFFICIENTS AS THE DENOMINATORS显示文摘The present paper proves that if f(x)∈C[0,1],changes its sign exactly l times at 0 | Dansheng Yu Songping Zhou | 2006 | Analysis in Theory and Applications2006，22，1： | 1 |
| 10 | Double trigonometric series with positive coefficients显示文摘 | Yu Dansheng | 2009 | Anal Math2009，35，2： | 1 |
| 11 | SOME NEW CONDITIONS IN FOURIER ANALYSIS AND APPLICATIONS显示文摘我们作为 monotonicity 状况的归纳在 Fourier 分析调查一些条件。特别,我们给 GBVS 的一些应用,序列满足条件并且。给词调音三角法的系列 - 一致集中 - L 鈥 ? 集中 AMS (2000 ) 题目分类 42A20 - 中国(10471130 ) 的 NSF 部分地支持的 42A32。近似理论和遥感应用上的国际会议上的邀请报告, Kungming,中国, | Songping Zhou Dansheng Yu Ruijun Le | 2007 | Analysis in Theory and Applications2007，23，1： | 1 |
| 12 | On a result of Flett for Cesáro matrices显示文摘 | Yu Dansheng | 2009 | Appl Math Lett2009，22，： | 1 |
| 13 | On Weighted Approximation by Modified Bernstein Operators for Functions with Singularities显示文摘Della Vecchia et al.(see [2]) introduced a kind of modified Bernstein operators which can be used to approximate functions with singularities at endpoints on[0,1]In the present paper, we obtain a kind of pointwise Stechkin-type inequalities for weighted approximation by the modified Bernsetin operators. | Meiling Wang Dansheng Yu | 2014 | Analysis in Theory and Applications2014，30，4： | 0 |
| 14 | WEIGHTED L^p-APPROXIMATION BY THE MODIFIED NEVAI OPERATORS显示文摘The present paper gives a Jackson type estimate for Nevai operators under weighted Lp norm, and establishes the direct and converse theorems in some proper Besov spaces. | Dansheng Yu Songping Zhou | 2005 | Analysis in Theory and Applications2005，21，3： | 0 |
| 15 | On Approximation by Neural Networks with Optimized Activation Functions and Fixed Weights显示文摘Recently,Li[16]introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights,and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs,for continuous function defined on bounded intervals.In the present paper,we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in[16].By using new methods,we also give right approximation rate estimations of the approximation by Li’s neural networks. | Dansheng Yu Yunyou Qian Fengjun Li | 2023 | Analysis in Theory and Applications2023，39，1： | 0 |
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