Inexact simultaneous projection method for solving bilevel equilibrium problems

Abstract

In this work we consider a bilevel equilibrium problem defined over the intersection of the fixed points set of demicontractive mappings. An inexact simultaneous projection method for solving the problem is introduced and its strong convergence is established under mild and standard conditions. Primary numerical illustrations in finite and infinite dimensional spaces with comparisons to related results in the literature, demonstrate the algorithm performances and emphasize its computational and theoretical advantages.