## 留言板

Banach空间内一类广义混合隐平衡问题组解的存在性和迭代算法

 引用本文: 丁协平. Banach空间内一类广义混合隐平衡问题组解的存在性和迭代算法[J]. 应用数学和力学, 2010, 31(9): 1001-1015.
DING Xie-ping. Existence and Algorithm of Solutions for a System of Generalized Mixed Implicit Equilibrium Problems in Banach Spaces[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1001-1015. doi: 10.3879/j.issn.1000-0887.2010.09.001
 Citation: DING Xie-ping. Existence and Algorithm of Solutions for a System of Generalized Mixed Implicit Equilibrium Problems in Banach Spaces[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1001-1015.

## Banach空间内一类广义混合隐平衡问题组解的存在性和迭代算法

##### doi: 10.3879/j.issn.1000-0887.2010.09.001

###### 作者简介:丁协平(1938- ),男,四川自贡人,教授(Tel:+86-28-84780952;E-mail:xieping_ding@hotmailcom).
• 中图分类号: O177.91;O178;O241.7

## Existence and Algorithm of Solutions for a System of Generalized Mixed Implicit Equilibrium Problems in Banach Spaces

• 摘要: 在Banach空间内引入和研究了一类新的广义混合隐平衡问题组．首先,对广义混合隐平衡问题组引入了Yosida逼近映射概念．利用此概念,考虑了一个广义方程问题组并证明了它与广义混合隐平衡问题组的等价性．其次,应用广义方程问题组,建议和分析了计算广义混合隐平衡问题组的近似解的迭代算法．在相当温和的条件下,证明了由算法生成的迭代序列的强收敛性．这些结果是新的并且统一和推广了这一领域内的某些最近结果．
•  [1] Blum E, Oettli W. From optimization and variational inequalities to equilibrium problems[J]. Math Student, 1994,63(1): 123-145. [2] Moudafi A, Théra M. Proximal and dynamical approaches to equilibrium problems[C]Lecture Notes in Economics and Mathematical Systems.477. Berlin: Springer,1999: 187-201. [3] Moudafi A. Mixed equilibrium problems: sensitivity analysis and algorithmic aspects[J]. Comput Math Appl, 2002, 44(8/9): 1099-1108. [4] Giannessi F, Maugeri A, Pardalos M. Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models[M]. Dordrecht: Kluwer Academic, 2001. [5] Giannessi F, Maugeri A. Variational Inequalities and Network Equilibrium Problems[M]. New York: Plenum, 1995. [6] Noor M A. Multivalued general equilibrium problems[J].J Math Anal Appl, 2003, 283(1): 140-149. [7] Noor M A. Auxiliary principle technique for equilibrium problem[J].J Optim Theory Appl, 2004, 122(2): 371-386. [8] Noor M A. Generalized mixed quasi-equilibrium problems with trifunction[J].Appl Math Lett, 2005, 18(5): 695-700. [9] Ding X P. Iterative algorithm of solutions for generalized mixed implicit equilibrium-like problems[J]. Appl Math Comput, 2005, 162(2): 799-809. [10] 丁协平, 林炎诚, 姚任之. 求解广义混合隐拟平衡问题的预测修正算法[J]. 应用数学和力学, 2006, 27(9): 1009-1016. [11] Xia F Q, Ding X P. Predictor-corrector algorithms for solving generalized mixed implicit quasi-equilibrium problems[J]. Appl Comput Math, 2007, 188(1): 173-179. [12] Tada A, Takahashi W. Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem[J]. J Optim Theory Appl, 2007, 133(3): 359-370. [13] Ceng L C, Yao J C. A hybrid iterative scheme for mixed equilibrium problems and fixed point problems[J]. J Comput Appl Math, 2008, 214(1):186-201. [14] Bigi G, Castellani M, Kassay G. A dual view of equilibrium problems[J].J Math Anal Appl, 2008,342(1): 17-26. [15] Colao V, Marino G, Xu H-K. An iterative method for finding common solutions of equilibrium and fixed point problems[J]. J Math Anal Appl, 2008, 344(2): 340-352. [16] Plubtieng S, Punpaeng R. A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings[J]. Appl Math Comput, 2008, 197(2): 548-558. [17] Chang S S, Lee H W J, Chan C K. A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization[J]. Nonlinear Anal, 2009, 70(9): 3307-3319. [18] Ceng L C, Al-Homidan S, Ansari Q H, Yao J C. An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings[J]. J Comput Appl Math, 2009, 223(2): 967-974. [19] Qin X L, Cho Y J, Kang S M. Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces[J]. J Comput Appl Math, 2009, 225(1): 20-30. [20] Jung J S. Strong convergence of composite iterative methods for equilibrium problems and fixed point problems[J]. Appl Math Comput, 2009, 213(2): 489-505. [21] Colao V, Acedo G L, Marino G. An implicit method for finding common solutions of variational inequalities and system of equilibrium problems and fixed points of infinite family of nonexpansive mappings[J]. Nonlinear Anal, 2009, 71(7/8): 2708-2715. [22] Huang N A, Lan H Y, Cho Y J. Sensitivity analysis for nonlinear generalized mixed implicit equilibrium problems with non-monotone set-valued mappings[J]. J Comput Appl Math, 2006, 196(2): 608-618. [23] Kazmi K R, Khan F A. Existence and iterative approximation of solutions of generalized mixed equilibrium problems[J]. Comput Math Appl, 2008, 56(5):1314-1321. [24] Ding X P, Ho J L. New iterative algorithm for solving a system of generalized mixed implicit equilibrium problems in Banach spaces[J]. Taiwanese J Math, this paper is available online at [25] 张石生. 变分不等式和相补问题理论及应用[J]. 上海:上海科学技术文献出版社, 1991. [26] Noor M A. Auxiliary principle for generalized mixed variational-like inequalities[J]. J Math Anal Appl,1997, 215(1): 78-85. [27] Ding X P. On generalized mixed variational-like inequalities[J]. J Sichuan Normal Univ, 1999,22(5): 494-503. [28] Ding X P, Tarafdar E. Existence and uniqueness of solutions for a general nonlinear variational inequality[J]. Appl Math Lett, 1995, 8(1): 31-36. [29] Ding X P. Generalized quasi-variational-like inclusions with nonconvex functions[J]. Appl Math Comput, 2001, 122(3): 267-282. [30] Ansari Q H, Yao J C. Iterative schemes for solving mixed variational-like inequalities[J]. J Optim Theory Appl, 2001, 108(3): 527-541. [31] Huang N J, Deng C X. Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities[J]. J Math Anal Appl, 2001, 256(2): 345-359. [32] Ding X P. Existence and algorithm of solutions for nonlinear mixed quasi-variational inequalities in Banach spaces[J]. J Comput Appl Math, 2003, 157(2): 419-434. [33] Ding X P. Existence and algorithm of solutions for mixed variational-like inequalities in Banach spaces[J]. J Optim Theory Appl, 2005, 127(2): 285-302. [34] Ding X P, Yao J C. Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces[J]. Comput Math Appl, 2005, 49(5/6): 857-869. [35] Ding X P, Yao J C, Zeng L C. Existence and algorithm of solutions for generalized strongly nonlinear mixed variational-like inequalities in Banach spaces[J]. Comput Math Appl, 2008, 55(4): 669-679. [36] Zeng L C, Guu S M, Yao J C. Three-step iterative algorithms for solving the system of generalized mixed quasi-variational-like inclusions[J]. J Comput Math Appl, 2007, 53(10): 1572-1581. [37] Zeng L C, Schaible S, Yao J C. Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequalities[J]. J Optim Theory Appl, 2005,124(3): 725-738. [38] Zeng L C, Guu S M, Yao J C. Iterative algorithm for completely generalized set-valued strongly nonlinear mixed variational-like inequalities[J]. J Comput Math Appl, 2005,50(5/6): 935-945. [39] Nadler S B. Multivalued contraction mapping[J]. Pacific J Math, 1969, 30: 475-488.

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##### 出版历程
• 收稿日期:  1900-01-01
• 修回日期:  2010-08-17
• 刊出日期:  2010-09-15

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