On equilibrium-like problems

Abstract

In this article we introduce a new class of equilibrium problems known as mixed quasi invex equilibrium (equilibrium-like) problems with trifunction. This class of equilibrium problems includes invex equilibrium problems, variational inequalities and variational-like inequalities as special cases. 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 mild conditions. Our results represent significant and important refinements of the previously known results.

Keywords:

• Variational-like inequalities
• Invex equilibrium problems
• Auxiliary principle
• Proximal methods
• Convergence
• Skew-symmetric functions

Keywords:

• AMS Subject Classifications:
• 49J40
• 90C33

Acknowledgment

This research is supported by the Higher Education Commission, Pakistan, through grant No. 1-28/HEC/HRD/2005/90.