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关于广义变分不等式与广义拟变分不等式

张从军

张从军. 关于广义变分不等式与广义拟变分不等式[J]. 应用数学和力学, 1993, 14(4): 315-325.
引用本文: 张从军. 关于广义变分不等式与广义拟变分不等式[J]. 应用数学和力学, 1993, 14(4): 315-325.
Zhang Cong-jun. Generalized Variational Inequalities and Generalized Quasi-Variational Inequalities[J]. Applied Mathematics and Mechanics, 1993, 14(4): 315-325.
Citation: Zhang Cong-jun. Generalized Variational Inequalities and Generalized Quasi-Variational Inequalities[J]. Applied Mathematics and Mechanics, 1993, 14(4): 315-325.

关于广义变分不等式与广义拟变分不等式

Generalized Variational Inequalities and Generalized Quasi-Variational Inequalities

  • 摘要: 本文在非常一般的框架下,建立了极大极小不等式,广义变分不等式和广义拟变分不等式,证明了解的存在定理,且它们是在非紧集上得到的,从而推广和改进了[3~13]中的相应结果.
  • [1] 张石生,《变分不等式和相补问题理论及应用》,上海科技文献出版社(1991).
    [2] 夏道行、杨亚力,《线性拓扑空间引论》、上海科技出版社(1986).
    [3] Allen,G.,Variational inequalities,complementarity problems and duality theorems,J.Math.Anal.Appl.,58(1977),1-10.
    [4] Bae,J.S.,W.K.Kim and K.K.Tan,Another generalization of Ky Fan’s minimax inequality and its applications.(submitted for publication).
    [5] Browder,F.E.,The fixed point theory of multi-valued mappings in topological vector spaces,Math.Ann.,177(1968),283-301.
    [6] Fan Ky.,Some properties of convex sets related to fixed point theorems,Math.Ann.,266(1984),519-537.
    [7] Shih,M.H.and K.K.Tan,Generalized quasi-variational inequalities in locally convex topological vector spaces,J.Math.Anal.Appl.,108(1985),333-343.
    [8] Shih,M.H.and K.K.Tan,A geometric property of convex sets with applications to minimax type inequalities and fixed point theorems,J.Austral.Math.Soc.,Ser.,A,45(1988),169-183.
    [9] Tan,K.K.,Comparison theorems on minimax inequalities Variational inequalities and fixed point theorems,J.London Math.Soc.,28(1983),555-562.
    [10] Browder,F.E.,A new generalization of the Schauder fixed point theorem,Math.Ann.,174(1967),285-290.
    [11] Shih,M.H.and K.K.Tan,Minimax inequalities and applications,Contemp.Math.,54(1986),45-63.
    [12] Hartman,P.and G.Stampacchia,On some nonlinear elliptic functional differential equations,Acta Math.,115(1966),271-310.
    [13] Kim,W.K.and K.K.Tan,A variational inequality in noncompact sets and its applications,Bull Austral.Math.Soc.(to appear).
    [14] Ding,X.P.,W.K.Kim and K.K.Tan,Equilibrium of noncompact generalized games with L-majorized preference correspondences,J.Math.Anal.Appl.(in press).
    [15] Ding,X.P.and K.K.Tan,Generalized variational inequalities and generalized quasi-variational inequalities,J.Math.Anal.Appl.,148(1990),497-508.
    [16] Rudin,W.,Functional Analysis,McGraw-Hill,Inc.(1973).
    [17] Shih,M.H.and K.K.Tan,Generalized bi-quasi-variational inequalities,J.Math.Anal.Appl.,143(1989),66-85.
    [18] Aubin,J.P.and A,Cellina,Differential Inclusions,Springer-Verlag,New York(1984).
    [19] Kneser,H.,Sur un theorem fondamental de la theorie des jeux.,C.R.Acad.Sci.Paris,234(1952),2418-2420.
    [20] Aubin,J.P.and I.Ekeland,Applied Nonlinear Analysis,Wiley-Interscience,New York(1984).
    [21] Himmelberg,C.J.,Fixed point of compact multifunctions,J.Math.Anal.Appl.,38(1972),205-207.
    [22] Ma,T.W.,Topological degree for set-valued compact vector field in local spaces,Dissortations Math.,92(1972),1-43.
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出版历程
  • 收稿日期:  1992-01-08
  • 刊出日期:  1993-04-15

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