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蔡钢
2015-04-28 14:12     (点击: )

个 人 信 息

姓名

蔡钢

性别

民族

出生日期

1984.10

政治面貌

中共党员

职称/职务

副教授

毕业学校

清华大学

学历

博士

博导/硕导

学科专业

基础数学

研究方向

Banach空间几何学

联系方式

caigang-aaaa@163.com

个人简历

蔡钢,重庆师范大学,数学学院,副教授, 20076月在重庆三峡学院获得理学学士学位,20079月进入湖北师范学院跟随胡长松教授攻读硕士研究生,20106月在湖北师范学院取得理学硕士学位,20109月进入清华大学跟随步尚全教授攻读基础数学专业博士研究生,20141月在清华大学取得理学博士学位,同时进入重庆师范大学数学学院工作,20149月破格副教授。主要研究方向为Banach 空间理论,不动点理论,向量值边值问题。 获得过2011年湖北省优秀硕士学位论文奖,2010-20112011-2012学年度清华大学综合一等奖学金,2012年度教育部博士研究生学术新人奖,2013年博士研究生国家奖学金,2014年北京市优秀毕业生。主持国家自然科学基金青年基金和重庆市自然科学基金项目各一项,主研两项国家自然科学基金面上项目、一项重庆市自然科学基金项目。已在Israel Journal of Mathematics, Mathematische NachrichtenTaiwanese Journal of MathematicsNonlinear AnalysisJournal of Computational and Applied MathematicsJournal of Global OptimizationMathematical and Computer ModellingApplied Mathematics LettersComputer & Mathematics with Applications,中国科学中英文版,数学学报英文版,数学物理学报中英文版等知名数学期刊上发表(含接收)30篇科研论文,其中27SCI论文。

主要研究项目

1 Banach 空间中非扩张映象的不动点性质及其迭代算法研究,国家自然科学基金委/青年基金项目,201501-201712,主持。

2 Banach空间中微分方程的适定性分析,重庆市科委/一般项目,201407-201606,主持。

3向量值边值问题最大正则性及其相关问题,国家自然科学基金委/面上项目,201201-201512,主研(3/7)

4算子代数上的非线性映射及其在量子信息中的应用,国家自然科学基金委/面上项目,201301-201612,主研(4/7)

5 几类具有孤立子和波破裂现象的非线性色散方程的若干问题研究,重庆市科委/一般项目,201407-201606,主研(2/3)

代表性成果

[1] G. Cai, C.S. Hu, Strong convergence theorems of modified Ishikawa iterative process with errors for an infinite family of strict pseudo-contractions, 

Nonlinear Analysis. 71 (2009) 6044-6053. (SCI)

[2] G. Cai, C.S. Hu, A hybrid approximation method for equilibrium and fixed problems for a family of infinite nonexpansive mappings and a monotone mapping, Nonlinear Analysis: Hybrid Systems. 3 (2009) 395-407. (SCI)

[3] G. Cai, C.S. Hu, On strong convergence by the hybrid method for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings, Fixed Point Theory and Applications. Volume 2009, Article ID 798319, 20 pages (SCI)

[4] C.S. Hu, G. Cai, Viscosity approximation schemes for fixed point problems and equilibrium problems and variational inequality problems, Nonlinear Analysis. 72 (2010) 1792-1808. (SCI)

[5] G. Cai, C.S. Hu, On the strong convergence of the implicit iterative processes of a finite family of relatively weak quasi-nonexpansive mappings, Applied Mathematics Letters. 23 (2010) 73-78. (SCI)

[6] G. Cai, C.S. Hu, Strong convergence theorems of general iterative process for a finite family of strict pseudo-contractions in q-uniformly smooth Banach spaces, Computers and Mathematics with Applications. 59 (2010) 149-160. (SCI)

[7] C.S. Hu, G. Cai, Convergence theorems for equilibrium problems and fixed point problems of a finite family of asymptotically k-strictly pseudocontractive mappings in the intermediate sense, Computers and Mathematics with Applications. 61 (2011) 79-93. (SCI)

[8] G. Cai and S. Bu, Approximation of common fixed points of a countable family of continuous pseudocontractions in a uniformly smooth Banach space, Applied Mathematics Letters, 24, 1998–2004, 2011. (SCI)

[9] G. Cai and S. Bu, A viscosity approximation scheme for finite mixed equilibrium problems and variational inequality problems and fixed point problems, Computer and Mathematics with Applications, 62, 440-454, (2011). (SCI)

[10] G. Cai and S. Bu, Strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in Banach spaces, Computer and Mathematics with Applications, 62, 2567-2579, 2011. (SCI)

[11] G. Cai and S. Bu, Hybrid algorithm for generalized mixed equilibrium problems and variational inequality problems and fixed point problems, Computer and Mathematics with Applications, 62, 4772-4782, 2011. (SCI)

[12] G. Cai and S. Bu, Convergence analysis for variational inequality problems and fixed point problems in 2-uniformly smooth and uniformly convex Banach spaces,

Mathematical and Computer Modelling, 55, 538-546, 2012. (SCI)

[13] G. Cai and S. Bu, Strong convergence theorems for general variational inequality problems and fixed point problems in q-uniformly smooth Banach spaces, Fixed Point Theory, 13, 383-402, 2012. (SCI)

[14] G. Cai and S. Bu, A viscosity scheme for mixed equilibrium problems, variational inequality problems and fixed point problems, Mathematical and Computer Modelling, 57, 1212-1226, 2013. (SCI)

[15] G. Cai and S. Bu, Strong and weak convergence theorems for general mixed equilibrium problems and variational inequality problems and fixed point problems in Hilbert spaces, Journal of Computational and Applied Mathematics, 247, 34-52, 2013. (SCI)

[16] G. Cai and S. Bu, Modified extragradient methods for variational inequality problems and fixed point problems for an infinite family of nonexpansive mappings in Banach spaces, Journal of Global Optimization, 55, 437-457, 2013. (SCI)

[17] G. Cai and  S. Bu, Strong convergence theorems for variational inequality problems and fixed point problems in uniformly smooth and uniformly convex Banach spaces, Journal of Global Optimization, 56, 1529-1542, 2013. (SCI)

[18] G. Cai and S. Bu, An iterative algorithm for a general system of variational inequalities and fixed point problems in q-uniformly smooth Banach spaces, 

Optimization Letters, 7, 267-287, 2013. (SCI)

[19] G. Cai and S. Bu, Krasnoselskii-type fixed point theorems with applications to Hammerstein integral equations in spaces, Mathematische Nachrichten, 286, 1452-1465, 2013. (SCI)

[20] G. Cai and S. Bu, Strong convergence theorems for variational inequality problems and fixed point problems in Banach spaces, Bulletin of the Malaysian Mathematical Sciences Society, (2) 36(2), 525–540, 2013. (SCI)

[21] G. Cai and S. Bu, Weak convergence theorems for general equilibrium problems and variational inequality problems and fixed point problems in Banach spaces, Acta Mathematica Scientia, 33B(1), 303-320, 2013. (SCI)

[22] S. Bu and G. Cai, Mild well-posedness of second order differential equations on the real line, Taiwanese Journal of Mathematics, 17, 143-159, 2013. (SCI)

[23] S. Bu and G. Cai, Solutions of second order degenerate integro-differential equations in vector-valued functional spaces, Science China Mathematics, 56 (5), 1059-1072, 2013. (SCI)

[24] 蔡钢,步尚全, Banach空间中关于非扩张映射的修改的Mann迭代算法的强收敛定理,数学物理学报,2014,34A(1):1-8.

[25] S. Bu and G. Cai, Well-posedness of second order degenerate integro-

differential equations in vector-valued function spaces. Quaestiones Mathematicae, accepted. (SCI)

[26] G. Cai and S. Bu, Periodic solutions of third-order degenerate differential equations in vector-valued functional spaces, Israel Journal of Mathematics, accepted.(SCI)

[27] 蔡钢, Banach 中二阶退化微分方程的周期解,中国科学:数学,已接收.

[28] 蔡钢,关于非扩张映射的不动点问题的粘性迭代算法的强收敛定理,数学物理学报,已接收

[29] G. Cai, Y. Shehu, An iterative algorithm for fixed point problem and convex minimization problem with applications, Fixed Point Theory and Applications, accepted. (SCI)

[30] G. Cai, Viscosity iterative algorithm for variational inequality problems and fixed point problems of strict pseudo-contractions in uniformly smooth Banach spaces, Acta Mathematica Sinica, English Seriesaccepted(SCI).

 

 

 

 

 

 

 

 

 

 

 

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