On inertial type self-adaptive iterative algorithms for solving pseudomonotone equilibrium problems and fixed point problems

Abstract

. In this paper, we study an inertial accelerated iterative algorithm with a self-adaptive stepsize for finding a common solution of an equilibrium problem involving a pseudomonotone bifunction and a fixed point problem of a quasi-nonexpansive mapping with a demiclosedness property in a real Hilbert space. The algorithm is based on the subgradient extragradient method and the inertial method and this algorithm does not require a prior knowledge of the Lipschitz type constants of the pseudomonotone bifunction. We establish a weak convergence theorem of the modified iterative method under some standard assumptions. We also give some numerical examples to demonstrate the efficiency and applicability of the new algorithm.