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Set-Valued Resolvent Equations and Mixed Variational Inequalities

✍ Scribed by Muhammad Aslam Noor; Khalida Inayat Noor; Th.M Rassias

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 211 KB
Volume: 220
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5893

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we introduce and study a new class of variational inequalities, which is called the generalized set-valued mixed variational inequality. The resolvent operator technique is used to establish the equivalence among generalized set-valued variational inequalities, fixed point problems, and the generalized setvalued resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area.

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