Extended general variational inequalities

✍ Scribed by Muhammad Aslam Noor

• Book ID: 104000516
• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 366 KB
• Volume: 22
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2008.03.007

✦ Synopsis

In this work, we introduce and consider a new class of general variational inequalities involving three nonlinear operators, which is called the extended general variational inequalities. Noor [M. Aslam Noor, Projection iterative methods for extended general variational inequalities, J. Appl. Math. Comput. ( ) (in press)] has shown that the minimum of nonconvex functions can be characterized via these variational inequalities. Using a projection technique, we establish the equivalence between the extended general variational inequalities and the general nonlinear projection equation. This equivalent formulation is used to discuss the existence of a solution of the extended general variational inequalities. Several special cases are also discussed.