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Zbl 1128.49010
Noor, Muhammad Aslam
Existence results for quasi variational inequalities. (English)
[J] Banach J. Math. Anal. 1, No. 2, 186-194, electronic only (2007). ISSN 1735-8787/e

Summary: It is well known that the quasi variational inequalities are equivalent to the fixed point problems. We use this equivalent alternative formulation to discuss the existence of a solution of quasi variational inequalities under some mild conditions. Since the quasi variational inequalities include variational inequalities, implicit complementarity problems and optimization problems as special cases, results proved in this paper continue to hold these problems. This shows that results proved in this paper can be viewed as an important and significant improvement and refinement of the previous results.

MSC 2000:: *49J40 Variational methods including variational inequalities
90C33 Complementarity problems
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: equivalence of quasi variational inequalities to fixed point theorems; implicit complementarity problems; optimization problems

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