基本介紹
個人經歷,主要成就,科研項目,出版著作,
個人經歷
哈爾濱工業大學理學博士學位。 南開大學陳省身數學研究所所博士後流動站出站。曾到美國華盛頓大學數學系等十七個國家和地區三十多所高校和科研機構科研合作和學術訪問。主持國家自然科學基金項目和教育部主要科研項目9項。在國際學術刊物諸如JFA, IJM等發表文章70多篇。培養博士生22人，碩士生53人。曾10多次應國際學術會議和全國性學術會議作特邀大會報告。
主要成就
(和吳從炘教授合作)證明了Preiss可微性定理-這一Preiss在國際數學家大會(1990)上的45分鐘報告主體結果在更廣義的框架下仍然立(JFA); (和Fabian教授合作）證明了：一個GDS與 一個可分空間的乘積仍然是GDS (PAMS); 發現了BANACH空間單位球球面的球覆蓋性質 (Israel. J. Math., Studia Math.) , Mazur intersection 性質的解析特徵(JFA)以及擾動保距映射的弱穩定性公式和強穩定性特徵(JFA)等. 自2001年來, 先後被諸如中國數學會學術年會、韓國數學會國際數學年會、華人數學家大會等十多次邀請作國際學術會議和全國性學術會議的大會邀請報告. 分別擔任（2008年）首屆中國數學會和美數學會聯合學術年會第十一分會中方主席和 (2010年) 首屆中國數學會和韓國數學會聯合學術年會泛函分析分會中方co-chair。自2001年來共主 持科學研究項目9項, 其中6項國家自然科學基金項目、1項教育部跨世紀優秀人培養計畫項目, 2項教育部博士點基金項目。2002年入選"教育部跨世紀優秀人才培養計畫" 。現任全國泛函分析空間理論學術聯絡組成員, 全國非線性泛函分析大會聯絡組成員, 全國空間理論和套用泛函分析大會副主席, 曾擔任國家自然科學基金委員會數理科學部特邀評審和中國數學會常務理事以及福建省數學會理事長。學術期刊《數學進展》《套用泛函分析學報》《數學研究》《數學研究期刊》《International Journal of Functional Analysis, Operator Theory and Applications 》 和《The Open Mathematics Journal》編委,《廈門大學學報》副主編, 美國 《MATH REVIEWS》評論員。
科研項目
(1) 主持的國家自然科學基金項目
1. BANACH空間的擾動保距映射和粗保距映射(2014.01-2017.12), 國家自然科學基金（面上）項目, 編號：11371296
2. 無窮維空間的嵌入幾何與粗幾何(2011.01-2013.12), 國家自然科學基金（面上）項目, 編號：11071201
3. BANACH空間的局部嵌入與粗幾何(2008.01-2010.12), 國家自然科學基金（面上）項目, 編號：10771175
4. 中國數學會2009年年會資助申請(2009.01-2009.12), 國家自然科學基金（專項）項目 編號：10926004
5. 無窮維LIPSCHITZ映射的微分分析與HAMILTON-JACOBI 方程( 2005.1-2007.12), 國家自然科學基金（面上）項目 編號: 10471114
6. 無窮維空間的分析結構和隨機度量的理論方法(2001.01--2003.12), 國家自然科學基金（面上）項目 編號：10071063
(2) 主持的教育部科研基金項目
7. 擾動保度量映射和粗保度量映射的存在穩定性(2014.01-2.16.12), 教育部博士點基金（博導類）, 編號：20130121110032
8. BANACH空間的局部嵌入與粗幾何 (2008.01-2010.12), 教育部博士點基金（博導類）, 編號：20070384046
9. 教育部跨世紀優秀人才培養計畫項目 (2002.01-2004.12)
出版著作
[53] Cheng, Lixin; Zhou, Yu, Approximation by DC Functions and Application to Representation of a Normed Semigroup, J. Convex Anal. 21 (2014), no. 3, 651-661.
[52] Cheng, Lixin; Dai, Duanxu; Dong, Yunbai; Zhou, Yu, Universal stability of Banach spaces for ɛ-isometries, Studia Math. 221(2014), 141- 149.
[51] Cheng, Lixin, Zhou, Yu, On perturbed metric-preserved mappings and their stability characterizations, J. Funct. Anal. 266(8) (2014), 4995-5015.
[50] Bao, Ling Xin; Cheng, Li Xin; Cheng, Qing Jin; Dai, Duan Xu On universally left-stability of ɛ-isometry, Acta Math. Sin., Engl. Ser. 29 ( 2013), no. 11, 2037-2046.
[49] Bao, Lingxin; Cheng, Lixin On statistical measure theory. J. Math. Anal. Appl. 407 (2013), no. 2, 413–424. 40A35 (28A12 40G15).
[48] Cheng, Lixin; Luo, Zhenghua; Zhou, Yu On super weakly compact convex sets and representation of the dual of the normed semigroup they generate. Canad. Math. Bull. 56 (2013), no. 2, 272–282. (Reviewer: Anatolij M.
[48] Cheng, Lixin; Luo, Zhenghua; Zhou, Yu On super weakly compact convex sets and representation of the dual of the normed semigroup they generate. Canad. Math. Bull. 56 (2013), no. 2, 272–282. (Reviewer: Anatolij M.
Plichko) 46B20 (46A55 46B50).
[47] Cheng, Lixin; Dai, Duanxu; Dong, Yunbai A sharp operator version of the Bishop-Phelps theorem for operators from ℓ 1 to CL-spaces. Proc. Amer. Math. Soc. 141 (2013), no. 3, 867–872. (Reviewer: Şafak Ömer Alpay) 46B28 (46B25 47B37).
[47] Cheng, Lixin; Dai, Duanxu; Dong, Yunbai A sharp operator version of the Bishop-Phelps theorem for operators from ℓ 1 to CL-spaces. Proc. Amer. Math. Soc. 141 (2013), no. 3, 867–872. (Reviewer: Şafak Ömer Alpay) 46B28 (46B25 47B37).
[46] Cheng, Lixin; Dong, Yunbai; Zhang, Wen On stability of nonlinear non-surjective ε -isometries of Banach spaces. J. Funct. Anal. 264 (2013), no. 3, 713–734. (Reviewer: Guimei An) 46B04 (47B65).
[45] Cheng, Li Xin; Dong, Yun Bai A quantitative version of the Bishop- Phelps theorem for operators in Hilbert spaces. Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 10, 2107–2114. (Reviewer: Alexey S. Tikhonov) 47A55 (46A32 47B15) .
[44] Chen, Lizhen; Cheng, Lixin Analytic characterizations of Mazur's intersection property via convex functions. J. Funct. Anal. 262 (2012), no. 11, 4731–4745. (Reviewer: Patrick N. Dowling) 46B20.
[43] Cheng, Lixin; Zhou, Yu On approximation by Δ -convex polyhedron support functions and the dual of cc(X) and wcc(X) . J. Convex Anal. 19 (2012), no. 1, 201–212. (Reviewer: Libor Veselý) 41A65 (46A20) .
[42] Cheng, Lixin A functional view of Lebesgue integration. Acta Anal. Funct. Appl. 13 (2011), no. 4, 349–350, 391. 26A42 (26-01) .
[41] Cheng, Lixin Erratum to: Ball-covering property of Banach spaces [MR2282371]. Israel J. Math. 184 (2011), 505–507. 46B20.
[40] Cheng, Lixin; Dong, Yunbai On a generalized Mazur-Ulam question: extension of isometries between unit spheres of Banach spaces. J. Math. Anal. Appl. 377 (2011), no. 2, 464–470. (Reviewer: Bentuo Zheng) 46B03
(46B04 46B20).
[39] Cheng, Lixin; Wang, Bo; Zhang, Wen; Zhou, Yu Some geometric and topological properties of Banach spaces via ball coverings. J. Math. Anal. Appl. 377 (2011), no. 2, 874–880. (Reviewer: Miguel Martín) 46B20.
[39] Cheng, Lixin; Wang, Bo; Zhang, Wen; Zhou, Yu Some geometric and topological properties of Banach spaces via ball coverings. J. Math. Anal. Appl. 377 (2011), no. 2, 874–880. (Reviewer: Miguel Martín) 46B20.
[38] Cheng, Lixin; Shi, Huihua A functional characterization of measures and the Banach-Ulam problem. J. Math. Anal. Appl. 374 (2011), no. 2, 558–565. (Reviewer: Richard Becker) 28A33 (28A12).
[37] Cheng, Lixin; Cheng, Qingjin; Luo, Zhenghua On some new characterizations of weakly compact sets in Banach spaces. Studia Math. 201 (2010), no. 2, 155–166. (Reviewer: Marián Fabian) 46B20 (58C20).
[36] Cheng, Lixin; Cheng, Qingjin More on convexity and smoothness of operators. J. Math. Anal. Appl. 371 (2010), no. 2, 407–413. (Reviewer: Sebastián Lajara) 46B20 (47B10) .
[35] Cheng, Lixin; Cheng, Qingjin; Wang, Bo; Zhang, Wen On super-weakly compact sets and uniformly convexifiable sets. Studia Math. 199 (2010), no.2, 145–169. (Reviewer: Vicente Montesinos Santalucía) 46B20 (46B03 46B50).
[34] Cheng, Lixin; Kadets, Vladimir; Wang, Bo; Zhang, Wen A note on ball- covering property of Banach spaces. J. Math. Anal. Appl. 371 (2010), no. 1, 249–253. 46B20.
[33] Cheng, Li Xin; Luo, Zheng Hua; Liu, Xue Fang; Zhang, Wen Several remarks on ball-coverings of normed spaces. Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 9, 1667–1672. (Reviewer: Jesús García-Falset) 46B20 (46B03).
[32] Cheng, LiXin; Shi, HuiHua; Zhang, Wen Every Banach space with a w ∗-separable dual has a 1+ε -equivalent norm with the ball covering property. Sci. China Ser. A 52 (2009), no. 9, 1869–1874. (Reviewer: Vicente Montesinos Santalucía) 46B03 (41A65 46B20).
[31] Cheng, Lixin; Lin, Guochen; Shi, Huihua On real-valued measures of statistical type and their applications to statistical convergence. Math. Comput. Modelling 50 (2009), no. 1-2, 116–122. (Reviewer: Cihan Orhan) 28A33 (40G15 46B15) .
[30] Cheng, Lixin; Cheng, Qingjin; Shi, Huihua Minimal ball-coverings in Banach spaces and their application. Studia Math. 192 (2009), no. 1, 15–27. (Reviewer: Miguel Martín) 46B04 (46B03 46B20) .
[29] Cheng, Lixin; Zhang, Wen A note on non-support points, negligible sets, Gâteaux differentiability and Lipschitz embeddings. J. Math. Anal. Appl. 350 (2009), no. 2, 531–536. 46B20 (46G05 49J50) .
[28] Cheng, LiXin; Lin, GuoChen; Lan, YongYi; Liu, Hui Measure theory of statistical convergence. Sci. China Ser. A 51 (2008), no. 12, 2285–2303. (Reviewer: Surjit Singh Khurana) 60B05 (28B99 40G99 46G99 46N30).
[27] Cheng, Li Xin; Liu, Xiao Yan; Zuo, Mai Fang A linear perturbed Palais-Smale condition for lower semicontinuous functions on Banach spaces. Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 11, 1853–1860. (Reviewer: Raffaella Servadei) 46G05 (47J30 49J45 58E05) .
[26] Cheng, LiXin; Cheng, QingJin; Liu, XiaoYan Ball-covering property of Banach spaces that is not preserved under linear isomorphisms. Sci. China Ser. A 51 (2008), no. 1, 143–147. (Reviewer: Henryk Hudzik) 46B20 (46B03).
[25] Cheng, Li-Xin; Li, Min Extreme points, exposed points, differentiability points in CL-spaces. Proc. Amer. Math. Soc. 136 (2008), no. 7, 2445–2451. (Reviewer: Warren B. Moors) 46B20 (46G05).
[25] Cheng, Li-Xin; Li, Min Extreme points, exposed points, differentiability points in CL-spaces. Proc. Amer. Math. Soc. 136 (2008), no. 7, 2445–2451. (Reviewer: Warren B. Moors) 46B20 (46G05).
[24] Cheng, Li Xin; Teng, Yan Mei Certain subsets on which every bounded convex function is continuous. Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 6, 1063–1066. (Reviewer: Ion Raşa) 26E15 (26B25 46B20 46G99) .
[23] Chen, Shaoxiong; Cheng, Linxin; Fabian, Marián Approximation of convex functions in Asplund generated spaces. J. Nonlinear Convex Anal. 8 (2007), no. 1, 81–85. (Reviewer: John R. Giles) 46B22 (41A65).
[22] Cheng, Lixin Ball-covering property of Banach spaces. Israel J. Math. 156 (2006), 111–123. (Reviewer: Marián Fabian) 46B20.
[21] Cheng, Linxin; Chen, Shaoxiong Smooth approximation of convex functions in Banach spaces. J. Math. Anal. Appl. 313 (2006), no. 2, 572– 580. (Reviewer: Marián Fabian).
[20] Cheng, Lixin; Teng, Yanmei Differentiability of convex functions on sublinear topological spaces and variational principles in locally convex spaces. Chinese Ann. Math. Ser. B 26 (2005), no. 4, 611–632. (Reviewer: Jesús Ferrer) 49J50 (26E15 46B20 46G05 46N10 49J53) .
[19] Borwein, Jonathan; Cheng, Lixin; Fabian, Marián; Revalski, Julian P.A one perturbation variational principle and applications. Set-Valued Anal. 12 (2004), no. 1-2, 49–60. (Reviewer: John R. Giles) 49J53 (46B20 46G05 49J40 49J50) .
[18] Cheng, Lixin; Teng, Yanmei A strong optimization theorem in locally convex spaces. Chinese Ann. Math. Ser. B 24 (2003), no. 3, 395–402. (Reviewer: Mircea Balaj) 49J50 (46G05 46N10 90C48) .
[17] Cheng, Lixin; Ruan, Yingbin; Teng, Yanmei Approximation of convex functions on the dual of Banach spaces. J. Approx. Theory 116 (2002), no. 1, 126–140. (Reviewer: J. Borwein) 46B20 (41A65 46G99) .
[16] Cheng, Lixin; Fabian, Marián The product of a Gateaux differentiability space and a separable space is a Gateaux differentiability space. Proc. Amer. Math. Soc. 129 (2001), no. 12, 3539–3541. (Reviewer: Warren B. Moors) 46B20 (46G05 58C20) .
[15] Cheng, Li-xin On the p -Asplund space of a Banach space. Acta Anal. Funct. Appl. 3 (2001), no. 2, 120–128. (Reviewer: Javier Gómez Gil) 46G05 (46B22).
[14] Cheng, Li-xin Differentiability property and perturbed optimization or variational principle in locally convex spaces. Acta Anal. Funct. Appl. 1 (1999), no. 3, 231–244. (Reviewer: Jörg Thierfelder) 49K40 (49J53 90C31 90C46).
[13] Cheng, Lixin; Wu, Congxin; Xue, Xiaoping; Yao, Xiaobo Convex functions, subdifferentiability and renormings. Acta Math. Sinica (N.S.) 14 (1998), no. 1, 47–56. (Reviewer: A. B. Németh) 46N10 (46B03 46B20 49J52 52A05 54C60).
[12] Lixin, Cheng; Shuzhong, Shi; Bingwu, Wang; Lee, E. S. Generic Fréchet differentiability of convex functions dominated by a lower semicontinuous convex function. J. Math. Anal. Appl. 225 (1998), no. 2, 389–400. (Reviewer: Nikolay V. Zhivkov) 49J50 (46G05 58C20).
[11] Cheng, Lixin; Shi, Shuzhong; Lee, E. S. Generic Fréchet differentiability of convex functions on non-Asplund spaces. J. Math. Anal. Appl. 214 (1997), no. 2, 367–377. 46G05 (46B22 49J50).
[10] Wu, Congxin; Cheng, Lixin; Ha, Minghu; Lee, E. S. Convexification of nonconvex functions and application to minimum and maximum principles for nonconvex sets. Comput. Math. Appl. 31 (1996), no. 7, 27–36. (Reviewer: Li Xin Cheng) 46N10 (46B10 49J50 49K27) .
[9] Cheng, Li Xin; Zhou, Yunchi; Zhang, Fong Danes' drop theorem in locally convex spaces. Proc. Amer. Math. Soc. 124 (1996), no. 12, 3699–3702. (Reviewer: John R. Giles) 46A55 (46B20).
[8] Cheng, Li Xin; Zhang, Feng Differentiability of convex functions and Asplund spaces. Acta Math. Sci. (English Ed.) 15 (1995), no. 2, 171–179. (Reviewer: John R. Giles) 46G05 (46B20 49J50).
[7] Wu, Cong Xin; Cheng, Li Xin Some characterizations of differentiability of convex functions on small set. Fasc. Math. No. 25 (1995), 187–196. (Reviewer: Nikolay V. Zhivkov) 49J50 (46N10 58C20).
[6] Wu, Cong Xin; Cheng, Li Xin Extensions of the Preiss differentiability theorem. J. Funct. Anal. 124 (1994), no. 1, 112–118. (Reviewer: Marcin Studniarski) 46G05 (46N10 49J52) .
[5] Wu, Cong Xin; Cheng, Li Xin A note on the differentiability of convex functions. Proc. Amer. Math. Soc. 121 (1994), no. 4, 1057–1062. (Reviewer: Javier Gómez Gil) 46G05 (49J50).
[4] Cheng, Li Xin; Li, Jian Hua; Nan, Chao Xun The Gateaux and Fréchet differentiability of continuous gauge functions on a Banach space. Adv. in Math. (China) 20 (1991), no. 3, 326–334.
[4] Cheng, Li Xin; Li, Jian Hua; Nan, Chao Xun The Gateaux and Fréchet differentiability of continuous gauge functions on a Banach space. Adv. in Math. (China) 20 (1991), no. 3, 326–334.
[3] Cheng, Li Xin; Chen, Lian Chang; Wei, Wen Zhan Eigenfunctions, and convexity moduli and smooth moduli of Banach spaces. J. Math. 10 (1990), no. 3
[2] Cheng, Li Xin Two remarks on smoothness of Banach spaces. J. Math.Res. Exposition 9 (1989), no. 2, 315–316. 46B20
[1] Cheng, Li Xin; Chen, Lian Chang Comment: "L p -orthogonality in Banach spaces'' [J. Math. Res. Exposition 4 (1984), no. 4, 31–35; MR0805889(87d:46022)] by Z. Liu. (Chinese) J. Math. Res. Exposition 7 (1987), no. 1, 175–176. 46B20
