Iterative Approximation For σ-nonstandard Equilibrium Trifunction

Abstract

We describe a new class of equilibrium issues, the -nonstandard equilibrium trifunction variational inequality (NSET). It employs a multivalued operator in the trifunction formulation. To overcome this problem, we can design a three-step iterative algorithm and apply the auxiliary principle technique (AUXPT). The method does not require projection. We construct a thorough error estimate and demonstrate that the iterative sequence converges to a solution when has three points of monotonicity. This framework contains specific examples of several well-known types of variational inequality and the equilibrium issues, such as the generalized mixed quasi trifunction variational inequality and the generalized equilibrium problem.