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.

Generalized Variational Inequalities and Generalized Quasi-Variational Inequalities

  • Received Date: 1992-01-08
  • Publish Date: 1993-04-15
  • Under much weaker hypotheses and in a more general setting some existence theorems of solutions to generalized variational inequalities, generalized quasi-varia-tional inequalities and minimax inequalities are established. The results presented in this paper generalize the corresponding results of[3-13]to the noncompact case, thus improving these results.
  • loading
  • [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.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2105) PDF downloads(534) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return