PARALLEL PROJECTION METHODS FOR SOLVING PROBLEM OF PSEUDO-MONOTONE EQUILIBRIUM AND A FINITE SYSTEM OF NON-EXPANSIVE MAPPINGS

Abstract

Fixed point problems and equilibrium problems have many applications and are
efficient tools in science, engineering, analytic structures and many other fields. The
equilibrium problem in particular is a very general mathematical problem that includes many
special cases such as optimization problems, integral inequality problems, fixed point problems,
etc. In this article, the authors will propose a weak convergent theorem for an algorithm for
finding common solutions of a pseudomonotone equilibrium problem and a finite system of
non-extended mappings in a real Hilbert space. Almost existing methods for solving this
problem require a strict assumption of the strong monotonicity or Lipschitz-type continuity of
the cost bifunction f . The idea of this algorithm is to combine the projection method and the
parallel splitting-up technique. At each iteration step, the authors need to use one projection
only and do not require to use any Lipschitz-type continuity condition of the bifunction.