Error bounds and stability of the projection method for strongly pseudomonotone equilibrium problems

ABSTRACT

In this paper, we establish lower and upper error bounds for strongly pseudomonotone equilibrium problems with and without Lipschitz condition. Our results generalize and improve some existing results in the literature. Also, we prove the stability of the projection method for this class of problems. The final error of the algorithm can be evaluated through the upper bound of errors in its steps. Some numerical experiments are presented to illustrate the obtained results.

Keywords:

• Equilibrium problem
• error bounds
• solution stability
• strong pseudomonotonicity
• Lipschitz-type continuity

AMS CLASSIFICATIONS:

• 65K10
• 65K15
• 90C25
• 90C33

Disclosure statement

No potential conflict of interest was reported by the author.