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Zbl 1190.49036
Noor, Muhammad Aslam
Projection iterative methods for extended general variational inequalities. (English)
[J] J. Appl. Math. Comput. 32, No. 1, 83-95 (2010). ISSN 1598-5865; ISSN 1865-2085/e

Summary: We introduce and study a new class of variational inequalities involving three operators, which is called the extended general variational inequality. Using the projection technique, we show that the extended general variational inequalities are equivalent to the fixed point and the extended general Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze a number of projection iterative methods for solving the extended general variational inequalities. We also consider the convergence of these new methods under some suitable conditions. Since the extended general variational inequalities include general variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems.

MSC 2000:: *49M15 Methods of Newton-Raphson, Galerkin and Ritz types
49J40 Variational methods including variational inequalities
90C33 Complementarity problems
93C10 Nonlinear control systems

Keywords: variational inclusions; fixed point problems; Wiener-Hopf equations; nonlinear operators; convergence criteria

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Zentralblatt MATH Berlin [Germany]