广义拟似变分不等式解的存在性*
Existence of Solutions for Generalized Quasi-Variational Like Inequalities
-
摘要: 本文在Hausdorff拓扑矢量空间的仿紧设置下对一类具有间断映象的广义拟似变分不等式证明了解的存在性定理.这些定理统一、改进和推广了广义拟变分不等式的许多最近结果.Abstract: In this paper, some existence theorems of solutions for a class of generalizedquasi-variational-like inequalities with discontinuous mappings are proved underparacompact setting in topological vector spaces. These theorems unify, improve andgeneralize many recent results.
-
[1] J.P,Aubin and I.Ekeland,Applied Nonlinear Analtlsis,John Wiley&Sons,New York (1984). [2] C.Baiocchi and A,Capelo,Variational and Quasivariational Inequalities,John Wiley & Sons,New York (1984). [3] D,Kinderlehrer and G,Stampacchi,An Introduction to Irariational Inequalities,Acad.Press,New York (1980). [4] D.Chan and J,S.Pang,The generalized quasi-variational inequalities,Math,Oiler,Res.,(1982),211-222. [5] P,T,Harker and J.S,Pang,Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory,algorithms and applications,Math,Program,Ser,B,4(1990),161-220. [6] M,A,Noor,General variational inequalities,Appl,Math,Lett.,1 (1988),119-122. [7] M.A,Noor,G eneral algorithm an d sensitivity for variational inequalities,J.Appl.Math,Stoch,Anal,,(1992),2 9-42. [8] M,A,Noor,K,I,Noor and T,M,Rassias,So me aspects of variational inequalities,J.Comput,Appl.Math,,47(1993),285-312. [9] J.C,Yao,General variational.inequalities in B anach spaces,Appl.Moth,Lett.,5(1) (1992),51-54. [10] J.C,Yao,On the general variational inequalities,J.Math,Ana.Appl.,174(1993),550-555. [11] J,C.Yao and J.S.Guo,Variational and generalized variational inequalities with discontinuous mappings,J.Math,Anal.Appl.,182(1994),371-392. [12] X,P,Ding and E,Tarafdar,Generalized nonlinear variational inequalities with non-m onotone set-valued mappings,Appl,Math,Lett.7(4) (1994),5-11. [13] 丁协平,一类广义变分不等式及应用,四川师范大学学报,17(6)(1994),10-16. [14] 丁协平,一类广义变分不等式解的存在性,烟台大学学报,2 (1995),15-22. [15] 丁协平,具有间断映象的隐变分不等式,四川师范大学学报,18(2)(1995),8-15 [16] J.Parida,M.Sahoo and A,Kumar,A variational-like inequality problem,BuI!.Austral.Math,Soc.,3(1989),225-231. [17] N,H,Dien,Some remarks on variational-like inequalities,Bull,Austral.Math,Soc,,4(1992),335-342. [18] A,H,Siddiqi,A,Khaliq and Q.H,Ansari,On variational-like inequalities,Ann,Sci,Quebec,18(1) (1994),95-104. [19] 丁协平,拟变分不等式和社会平衡,应用数学和力学,12(7) (1991),599-606. [20] 20 W,W,Hogan,Point-to-set maps in mathematical programming,SIAM Rev,,1(1973),591-603. [21] M,H,Shih and K.K,Tan,Covering theorems of convex sets related fixed pint theorems,in Nonlinear and Convex Andhsis,Marcel Dekker Incc.New York(1987),235-244. [22] J,X,Zhou and G.Chen,Diiagonzl convexity conditions for problems in convex analysis and quasi-variational inequalities,J.Math,Anal.Appl.,132 (1988),213-225. [23] H.Kneser,Suruti théoéme; fondamantal de la théorie des jeux,C,R,Acad,Sci,Paris,23(1952),2418-2420. [24] J,C.Yao,Generalized-quasi-vzriational inequality problems with discontinuous mappings,Math,Opera.Res,,20(2) (1005),965-478. [25] O,H,Merrill,Applications and extcr.sions of an algorithm that computes fixed points of certrain upper semi-continuous point-to-set mappings,Ph.D,Thesis,Univ,of Michigan,Ann Arbor,MI,(1972).
点击查看大图
计量
- 文章访问数: 2447
- HTML全文浏览量: 27
- PDF下载量: 693
- 被引次数: 0