个 人 信 息

姓名

蔡钢

性别

男

民族

汉

出生日期

1984.10

政治面貌

中共党员

职称/职务

教授

毕业学校

清华大学

学历

博士

博导/硕导

硕导

学科专业

基础数学

研究方向

Banach空间理论、向量值边值问题

联系方式

caigang-aaaa@163.com

个人简历

蔡钢，重庆师范大学，数学科学学院，教授，  2007年6月在重庆三峡学院获得理学学士学位，2007年9月进入湖北师范学院跟随胡长松教授攻读硕士研究生，2010年6月在湖北师范学院取得理学硕士学位，2010年9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，2014年1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，2014年9月破格副教授，2018年9月破格教授。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，2010-2011，2011-2012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面上基金、国家自然科学基金青年基金各一项、重庆市自然科学基金项目两项、重庆市教委项目两项，重庆市青年骨干教师项目一项，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、Pacific Journal of Mathematics、Proceedings of the Edinburgh Mathematical Society、Journal of Fourier  Analysis and Applications、Mathematische Nachrichten、Results in Mathematics、Expositiones  Mathematicae、Canadian  Mathematical Bulletin、Taiwanese Journal of Mathematics、Quaestiones Mathematicae、Journal of Evolution  Equations、Science  China Mathematics、Journal of Computational and Applied Mathematics、Numerical Algorithms、Mathematical and  Computer Modelling、Applied Mathematics Letters、Journal of Global Optimization、Journal of Optimization  Theory and Applications、Optimization Letters、Nonlinear Analysis、Computer and Mathematics with Applications、中国科学、数学学报、数学物理学报等国内外知名数学期刊上发表(含接收)40多篇科研论文。 

主要研究项目

1 向量值函数空间上退化微分方程的适定性，国家自然科学基金/面上基金项目，201801-202112，主持, 48万，在研。

2  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/青年基金项目，201501-201712，主持，22万，结题。

3  Banach空间中几类退化微分方程的适定性分析，重庆市科委/基础与前沿研究计划项目，201707-202006，主持，5万，在研。

4  Banach空间中微分方程的适定性分析，重庆市科委/基础与前沿研究计划项目，201407-201606，主持,5万，结题。

5  非线性算子的迭代算法研究，重庆市教委/教委科学技术项目，201701-201901，主持,3万，在研。

6  Banach空间中非线性算子与变分不等式的迭代逼近问题，重庆市教委/教委科学技术项目，201507-201706，主持,3万，结题。

7  Banach空间中几类微分方程的适定性研究，重庆市教委/重庆市高等学校青年骨干教师资助计划项目，201507-201706，主持,6万，在研。

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] 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)

[4] 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)

[5] 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)

[6] 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)

[7] 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 (2011) 1998–2004.  (SCI)

[8] 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 (2011) 440-454. (SCI)

[9] 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 (2011) 2567- 2579. (SCI)

[10] 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  (2011) 4772-4782. (SCI)

[11] 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 (2012) 538-546.  (SCI)

[12] 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 (2012)  383-402. (SCI)

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

[14] 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 (2013) 34-52. (SCI)

[15] 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 (2013) 437-457. (SCI)

[16] 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 (2013) 1529-1542. (SCI)

[17] 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 (2013)  267-287. (SCI)

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

[19] 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) (2013) 525–540.  (SCI)

[20] 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. 33 B(1)  (2013) 303-320. (SCI)

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

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

[23] S. Bu* and G. Cai, Well-posedness of second order  degenerate integro- differential equations in vector-valued function spaces. Quaestiones  Mathematicae. 38 (2015) 349-368. (SCI)

[24] 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 Series. 31(9) (2015) 1435-1448. (SCI).

[25] G. Cai*, S. Bu, Periodic solutions of third-order  degenerate differential equations in vector-valued functional spaces,  Israel Journal of Mathematics. 212 (2016) 163-188. (SCI)

[26] G. Cai*, S. Bu, Well-posedness of second order  degenerate integro-differential equations with infinite delay in  vector-valued function spaces, Mathematische Nachrichten. 289 (2016)  436-451. (SCI).

[27] G. Cai*, Y. Shehu, O. S. Iyiola, Iterative algorithms for  solving variational inequalities and fixed point problems for asymptotically  nonexpansive mappings in Banach spaces, Numerical Algorithms. 73  (2016) 869-906. (SCI)

[28] S. Bu, G. Cai*,well-posedness of second order  degenerate differential equations in Holder continuous function spaces,  Expositiones Mathematicae. 34 (2016) 223- 236. (SCI)

[29] G. Cai*, S. Bu, Periodic solutions of third-order  integro-differential equations in vector-valued functional spaces, Journal of Evolution  Equations. 17 (2017) 749- 780. (SCI)

[30] S. Bu, G. Cai*, Well-posedness of second-order  degenerate differential equations with finite delay, Proceedings of the  Edinburgh Mathematical Society. 60 (2017) 349-360. (SCI)

[31] S. Bu, G. Cai*, Well-posedness of second order  degenerate differential equations with finite delay in vector-valued function  spaces, Pacific Journal of Mathematics. 288(1) (2017) 27-46. (SCI)

[32] S. Bu, G. Cai*, Well-posedness of degenerate  differential equations with fractional derivative in vector-valued functional  spaces, Mathematische Nachrichten. 290 (5-6) (2017) 726-737. (SCI)

[33] S. Bu, G. Cai*, Well-posedness of fractional  degenerate differential equations with infinite delay in vector-valued  functional spaces, Journal of Integral Equations and Applications.  29(2) (2017) 297-323. (SCI)

[34] G. Cai*, Y. Shehu and O. S. Iyiola, Viscosity  iterative algorithms for fixed point problems of asymptotically nonexpansive  mappings in the intermediate sense and variational inequality problems in  Banach spaces, Numerical Algorithms.76 (2017) 521-553. (SCI)

[35] G. Cai*, Y. Shehu and O. S. Iyiola, Modified viscosity  implicit rules for nonexpansive mappings in Hilbert spaces, Journal of  Fixed Point Theory and Applications. 19 (2017) 2831-2846. (SCI)

[36] G. Cai*, Y. Shehu and O. S. Iyiola, Strong convergence  results for variational inequalities and fixed point problems using modified  viscosity implicit rules, Numerical Algorithms.77 (2018) 535-558.  (SCI)

[37] S. Bu, G. Cai*, Periodic solutions of second order degenerate differential  equations with finite delay in Banach spaces, Journal of Fourier Analysis  and Applications.25 (2019)  32-50. (SCI)

[38]  S. Bu, G. Cai*, Hölder continuous solutions of degenerate differential  equations with finite delay, Canadian Mathematical Bulletin.61(2018)  240-251.(SCI)

[39]  S. Bu, G. Cai*, Periodic solutions of second order degenerate  differential equations with delay in Banach spaces, Canadian  Mathematical Bulletin.61(2018) 717-737. (SCI)

[40] G. Cai, A. Gibali*, O. S. Iyiola,Y. Shehu, A new double-projection  method for solving variational inequalities in Banach Space, Journal  of Optimization Theory and Applications. 178(2018)219-239. (SCI)