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  Volume 8, Issue 1, Article 6
General System of Strongly Pseudomonotone Nonlinear Variational Inequalities Based on Projection Systems

    Authors: Ram U. Verma,  
    Keywords: Strongly pseudomonotone mappings, Approximation solvability, Projection methods, System of nonlinear variational inequalities.  
    Date Received: 26/02/06  
    Date Accepted: 11/12/06  
    Subject Codes:

49J40, 65B05, 47H20.

    Editors: Ram N. Mohapatra,  

Let $ K_1$ and $ K_2,$ respectively, be non empty closed convex subsets of real Hilbert spaces $ H_1$ and $ H_2.$ The $ Approximation-solvability$ of a generalized system of nonlinear variational inequality $ (SNVI)$ problems based on the convergence of projection methods is discussed. The SNVI problem is stated as follows: find an element $ (x^*,y^*)$ in K_{1}$ times K_{2} $ such that

$ displaystyle $ left$ langle $ rho S(x^*,y^*), x-x^*$ right$ rangle  $ geq 0,$ $ displaystyle $ forall x$ in K_1$ and for $ displaystyle $ rho>0, $
$ displaystyle $ left$ langle $ eta T(x^*,y^*), y-y^*$ right$ rangle  $ geq0,$  $ forall y$ in K_2$ and for $ displaystyle $ eta>0, $
where $ S:K_{1}$ times K_{2}$ rightarrow H_1$ and $ T:K_{1}$ times K_{2}$ rightarrow H_2$ are nonlinear mappings.

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