Acta mathematica scientia, Series B >
NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS
Received date: 2008-09-13
Revised date: 2010-04-07
Online published: 2011-05-20
Supported by
This project was supported by the Scientific Research Fun of Sichuan Normal University (09ZDL04) and the Sichuan Province Leading Academic Discipline Project (SZD0406).
In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure. By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.
DING Xie-Ping . NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS[J]. Acta mathematica scientia, Series B, 2011 , 31(3) : 1142 -1154 . DOI: 10.1016/S0252-9602(11)60305-6
[1] Hai N X, Khanh P Q. Systems of set-valued quasivariational inclusion problems. J Optim Theory Appl, 2007, 135: 55–67
[2] Lin L J, Ansari Q H, Huang Y J. System of vector quasi-variational inclusions with some applications. Nonlinear Anal, 2008, 69(9): 2812–2824
[3] Lin L J, Tu C I. The studies of systems of variational inclusions problems and applications. Nonlinear Anal, 2008, 69(7): 1981–1998
[4] Lin L J. System of generalized vector quasi-equilibrium problems with applications to fixed point theorems for a family of nonexpansive multivalued mappings. J Glob Optim, 2006, 34: 15–32
[5] Luc D T, Tan N X. Existence conditions in variational inclusions with constraints. Optimization, 2004, 53: 505–515
[6] Tan N X. On the existence of solutions of quasi-variational inclusions. J Optim Theory Appl, 2004, 123: 619–638
[7] Hai N X, Khanh P Q. The solution existence of general variational inclusion problems. J Math Anal Appl, 2007, 328: 1268–1277
[8] Ding X P. System of generalized vector quasi-equilibrium problems in locally FC-spaces. Acta Math Sinica, 2006, 22(5): 1529–1538
[9] Ding X P. Generalized game and system of generalized vector quasi-equilibrium problems in G-convex spaces. Acta Math Sci (Chinese Ser), 2006, 26(4): 506–515
[10] Ding X P. System of generalized vector quasi-equilibrium problems on product FC-spaces. Acta Math Sci, 2007, 27B(3): 522–534
[11] Ding X P. The generalized game and system of generalized vector quasi-equilibrium problems in locally FC-uniform spaces. Nonlinear Anal, 2008, 68(4): 1028–1036
[12] Ding X P. Existence of solutions for systems of generalized vector quasi-equilibrium problems in FC-spaces. Acta Math Sinica, (Chinese Series), 2009, 52(5): 919–930
[13] Ding X P. New system of generalized vector quasi-equilibrium problems in product FC-spaces. J Global Optim, 2010, 46(1): 133–146
[14] Ding X P. Mathematical programs with system of generalized vector quasi-equilibrium constraints in FC- spaces. Acta Math Sci, 2010, 30B(4): 1257–1268
[15] Ding X P. Maximal elements of GKKM-majorized mappings in product FC-spaces and applications (I). Nonlinear Anal, 2007, 67(3): 963–973
[16] Ding X P. Maximal element theorems in product FC-spaces and generalized games. J Math Anal Appl, 2005, 305(1): 29–42
[17] Horvath C D. Contractibility and generalized convexity. J Math Anal Appl, 1991, 156: 341–357
[18] Park S, Kim H. Foundations of the KKM theory on generalized convex spaces. J Math Anal Appl, 1997,
209: 551–571
[19] Ben-El-Mechaiekh H, Chebbi S, Flornzano M, Llinares J V. Abstract convexity and fixed points. J Math
Anal Appl, 1998, 222: 138–150
[20] Ding X P. Maximal elements and generalized games involving condensing mappings in locally FC-uniform
spaces and applications (I). Appl Math Mech, 2007, 28(12): 1561–1568
[21] Ding X P. Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and
nonconvex domains and ranges in topological spaces. Nonlinear Anal, 2009, 70(2): 881–889
[22] Aliprantis C D, Border K C. Infinite Dimensional Analysis. New York: Springer-Verlag, 1994
[23] Luc D T. Theory of Vector Optimization, Lectures Notes in Economics and Mathematical Systems, Vol
319. Berlin: Springer Verlag, 1989
[24] Takahashi W. Nonlinear Functional Analysis. Yokohama, Japan: Yokohama Publishers, 2000
/
| 〈 |
|
〉 |