Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 3, Pages 235-244

Hemiequilibrium problems

Muhammad Aslam Noor

Etisalat College of Engineering, P.O. Box 980, Sharjah, United Arab Emirates

Received 22 November 2003; Revised 17 May 2004

Copyright © 2004 Muhammad Aslam Noor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a new class of equilibrium problems, known as hemiequilibrium problems. Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity. As a special case, we obtain a new method for hemivariational inequalities. Since hemiequilibrium problems include hemivariational inequalities and equilibrium problems as special cases, the results proved in this paper still hold for these problems.