厦门大学数学学院师资队伍
School of Mathematical Sciences Xiamen University
师资队伍

程立新,男,数学科学学院教授、博士生导师,厦门大学陈景润特聘教授。

专业方向为:泛函分析、 凸分析、Banach空间几何、非线性几何 。

哈尔滨工业大学理学博士学位。 南开大学陈省身数学研究所所博士后流动站出站。曾到美国华盛顿大学数学系等十七个国家和地区三十多所高校和科研机构科研合作和学术访问。主持国家自然科学基金项目和教育部主要科研项目9项。在国际学术刊物诸如JFA,  IJM等发表文章70多篇。培养博士生23人,硕士生55人。曾10多次应国际学术会议和全国性学术会议作特邀大会报告。

主要学术贡献为:(和吴从炘教授合作)证明了Preiss可微性定理-这一Preiss在国际数学家大会(1990)上的45分钟报告主体结果在更广义的框架下仍然立;  (和Fabian教授合作)证明了:一个GDS与 一个可分空间的乘积仍然是GDS ; 发现了BANACH空间单位球球面的球覆盖性质; Mazur intersection 性质的解析特征以及扰动保距映射的弱稳定性公式和强稳定性特征等。自2001年来,  曾十多次邀请作国际学术会议和全国性学术会议的大会邀请报告, 例如,在中国数学会学术年会作邀请报告,华人数学家大会作45分钟报告; 作为大会报告人(plenary speaker)分别在 韩国数学会浦项国际数学年会、第五届Banach和函数空间国际会议(ISBFS2015, 日本)上作大会特邀报告等。分别担任(2008年)首届中国数学会和美数学会联合学术年会第十一分会中方主席和 (2010年) 首届中国数学会和韩国数学会联合学术年会泛函分析分会中方co-chair。自2001年来共主 持科学研究项目10项, 其中7项国家自然科学基金项目、1项教育部跨世纪优秀人培养计划项目, 2项教育部博士点基金(博导类)项目。2002年入选"教育部跨世纪优秀人才培养计划" 。现任全国泛函分析空间理论学术联络组成员, 中国数学会非线性泛函分析专业委员会委员,  曾担任全国空间理论学术联络组主任,全国泛函分析空间理论和应用泛函分析大会副主席, 国家自然科学基金委员会数理科学部特邀评委,中国数学会常务理事以及福建省数学会理事长。《数学进展》等六个国际国内数学学术期刊编委,《厦门大学学报》副主编。

 

一. 科研项目

(1)  主持的国家自然科学基金项目

 

1. 巴拿赫空间的嵌入理论及其应用(2017.01-2018.12),  国家自然科学基金 (海外及港澳学者合作研究基金 外方主持人 郑本拓 中方合作者 程立新)项目, 编号: 11628102

2. BANACH空间的扰动保距映射和粗保距映射(2014.01-2017.12), 国家自然科学基金(面上)项目,  编号:11371296

3. 无穷维空间的嵌入几何与粗几何(2011.01-2013.12),  国家自然科学基金(面上)项目,  编号:11071201

4. BANACH空间的局部嵌入与粗几何(2008.01-2010.12),  国家自然科学基金(面上)项目,  编号:10771175

5. 中国数学会2009年年会资助申请(2009.01-2009.12),  国家自然科学基金(专项)项目 编号:10926004

6. 无穷维LIPSCHITZ映射的微分分析与HAMILTON-JACOBI 方程( 2005.1-2007.12),  国家自然科学基金(面上)项目  编号: 10471114

7. 无穷维空间的分析结构和随机度量的理论方法(2001.01--2003.12),  国家自然科学基金(面上)项目  编号:10071063

(2) 主持的教育部科研基金项目

8. 扰动保度量映射和粗保度量映射的存在稳定性(2014.01-2.16.12),  教育部博士点基金(博导类),  编号:20130121110032

9.  BANACH空间的局部嵌入与粗几何 (2008.01-2010.12),  教育部博士点基金(博导类),  编号:20070384046

10.  教育部跨世纪优秀人才培养计划项目 (2002.01-2004.12)

 

二. 主要作品

[61] Cheng, Lixin; Cheng, Qingjin; Tu, Kun; Zhang, Jichao; Zhang, Wen,   On super weak compactness  of subsets and equivalences in Banach spaces, Journal of Convex Analysis, 25: 3 (2018).

[60]  Cheng , Lixin; Cheng,  Qingjin; Shen,  Qinrui ;  Tu, Kun;  Zhang,  Wen   A new approach to measures of noncompactness of Banach spaces, Studia Mathematica
MSC: 47H08, 46B42, 46B50, 46B04. DOI: 10.4064/sm8448-2-2017;  Opublikowany online: 7 July 2017.

[59] Cheng, Lixin; Shen, Qinrui; Zhang, Wen, Zhou, Yu  More on stability of almost surjective ε-isometries of Banach spaces, SCIENCE CHINA Mathematics, 60(2017), no.2,  277-284. 


[58] Cheng, Li Xin; Lin, Li Hua; Zhou, Xian Geng; Statistical convergence and measure convergence generated by a single statistical measure. Acta Math. Sin. (Engl. Ser.) 32 (2016),  no. 6, 668–682.
 

[57]  Cheng, Li Xin; Luo, Zheng Hua; Zhang, Wen; Zheng, Ben Tuo;  On proximinality of convex sets in superspaces. Acta Math. Sin. (Engl. Ser.) 32 (2016), no. 6, 633–64.

[56] Cheng, Lixin; Tu, Kun; Zhang, Wen  On weak stability of ε-isometries on wedges and its applications. J. Math. Anal. Appl. 433 (2016), no. 2, 1673–1689. 

[55] Cheng, Lixin; Cheng, Qingjin; Tu, Kun; Zhang, Jichao  A universal theorem for stability of ε-isometries of Banach spaces. J. Funct. Anal. 269 (2015), no. 1, 199–214.

[54] Cheng, Lixin; Cheng, Qingjin; Zhang, Jichao  On super fixed point property and super weak compactness of convex subsets in Banach spaces. J. Math. Anal. Appl. 428 (2015), no. 2, 1209–122.

[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. 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). 
 

[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. 
 

[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). 
 

[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.

[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 
  

 三. 学生培养

1999级 (1999.9--2002.7)     博士生    滕岩梅

2000级 (2000.9--2003.7)     博士生    阮颖彬               

                                                        硕士生    陈晓锋 罗正华 沈喜生

2001级 (2001.9--2004.7)     博士生   陈绍雄

                                                    

2002级 (2002.9--2005.7)           硕士生   付瑞瑜 骆道忠 谢元福 叶宏波

2003级(2003.9--2006.7)     博士生   沈喜生

                                                       硕士生   蓝永艺 卢允照 施慧华 张Xiao晶 陈 彬

2004级(2004.9--2007.7)     博士生   程庆进

                                                       硕士生   李 敏 林丽华 刘小燕 刘雪芳 柳 辉  王 波 

                                                                 杨国志 张 敏 周仙耕 左麦芳

2005级(2005.9--2008.7)    博士生  林国琛 张 文 张云南

                                                       硕士生  王 琨(2006.9--2008.7)

2006级(2006.9--2009.7)    博士生  罗正华 施慧华

                                                       硕士生  金翠华 王 琨 杨晓颍 张 洁 周 宇

2007级(2007.9--2010.7)    博士生  王 波

                                                       硕士生  鲍玲鑫 李艺珍 许康康

2008级(2008.9--2011.7)    博士生  董云柏

                                                       硕士生  戴端旭(直攻博) 李青霞(2014) 尹文明(2014) 张 晟  张小凤

2009级(2009.9--2012.7)    博士生  陈丽珍 周宇

                                                      硕士生  陈 婷 涂 昆 徐 佳 周田虎

2010级(2010.9--2013.7)    博士生  鲍玲鑫

                                                      硕士生   陈 波 陈婉贞 陈 颖

2011级 (2011.9--2014. 9) 博士生    戴端旭

                                                     硕士生   方权清(直攻博) 吴泽浩

2012级(2012.9--2015)       博士生   涂 昆    张吉超

                                                      硕士生   高绍阳 罗思捷(直攻博) 孙晓梅 王见见

2013级 (2013.9--)                博士生   沈钦锐

                                                      硕士生   苏丽丽  卫 倩  

2014级(2014.9--)                 博士生  方权清   罗思捷  孙龙发

                                                      硕士生  林  霞    沈思思

2015级(2015.9--)                 博士生  艾合买提. 阿不来提  

                                                      硕士生   陈炯阳  何五一

自2016级起,博士生由导师组集体指导,导师组成员为 程立新(组长),程庆进,张 文

2016级(2016.9--)                博士生 王见见  许康康 郑哲明   

                                                      硕士生  龚 琳    黄昌池

 

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    博士后    陈东阳 (2005--2007)    伊继金 (2010--2014)   蓝永艺(2014--)

 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    本科生  (2005届)    赖龙生   王焰金

                  (2007届)     程秋盛   李 茂     李艺珍 沈钦锐

                  (2008届)     陈建聪   刘晓力   秦 丹   张 晟

                  (2009届)     孙 晨     游 佳     周琛子

                  (2010届)     党 珏     阮 洁     周晓雪

                  (2011届)     吕龙祥   吕卓易   谭 帅

                  (2012届)     潘英通   许雨顺   叶其乐

                  (2016届)     贺    颖    姚犁云

                  (2017届)     胡志芳    赵  馨

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本科拔尖班人才计划

                 (2017届)      胡志芳      赵  馨

 

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中学英才计划  (2015-2016) 陈家祺  陈静远  易世铭   

 

 

 
 
 
简介
 
系别:
数学与应用数学系
办公室:物机数学615
教师:程立新
职称:教授
职务:教师
Phone:2580666
Email:
lxcheng@xmu.edu.cn
研究方向:
泛函分析,凸分析,Banach 空间几何, 无穷维非线性几何