IJPAM: Volume 13, No. 1 (2004)

INVEX $\epsilon-$EQUILIBRIUM
PROBLEMS WITH TRIFUNCTION

Muhammad Aslam Noor
Etisalat College of Engineering
P.O. Box 980, Sharjah, UNITED ARAB EMIRATES
e-mail: noor@ece.ac.ae


Abstract.In this paper, we introduce and investigate a new class of equilibrium problems, known as invex $\epsilon $-equilibrium problems with trifunction in the setting of invexity. We use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under some mild conditions. Our results represent significant and important refinements of the previously known results. Since invex $\epsilon $-equilibrium problems include invex equilibrium problems, variational inequalities and variational-like inequalities as special cases, results obtained in this paper continue to hold for these problems.

Received: March 15, 2004

AMS Subject Classification: 49J40, 90C30

Key Words and Phrases: variational-like inequalities, invex equilibrium problems, auxiliary principle, proximal methods, convergence

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 1