Full Text: PDF
Received August 5, 2020; Accepted January 19, 2021; Published February 5, 2021
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.
How to Cite this Article:
F.U. Ogbuisi, O.S. Iyiola, J.M.T. Ngnotchouye, T.M.M. Shumba, On inertial type self-adaptive iterative algorithms for solving pseudomonotone equilibrium problems and fixed point problems, Journal of Nonlinear Functional Analysis, Vol. 2021 (2021), Article ID 4, pp. 1-18.