Abstract
The fixed point technique is used to prove the existence of a solution for a class of variational inequalities related to odd order boundary value problems, and to suggest a general algorithm. We also study the sensitivity analysis for these variational inequalities and complementarity problems using the projection technique. Several special cases are discussed, which can be obtained from our results.
Highlights
Variational inequality theory is a very useful and effective technique for studying a wide class of problems in a unified natural and general framework
We study the qualitative behavior of the solution of the variational inequalities when the given operator and the feasible convex set vary with a parameter
Using the fixed point technique of Glowinski, Lions and Tremolieres [3], and Noor [7,8], we prove the existence of a solution of this variational inequality
Summary
Variational inequality theory is a very useful and effective technique for studying a wide class of problems in a unified natural and general framework This theory has been extended and generalized in several directions using new and powerful methods that have led to the solution of basic and fundamental problems previously thought to be inaccessible. Using the fixed point technique of Glowinski, Lions and Tremolieres [3], and Noor [7,8], we prove the existence of a solution of this variational inequality This approach enables us to suggest and analyze a general algorithm for these variational inequalities. The existence of the solution of variational inequality problem is studied in Section 3 using the fixed point method along with a general algorithm.
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