A new iterative algorithm for solving some nonlinear problems in Hilbert spaces

Volume 13, Issue 3, pp 119--132 http://dx.doi.org/10.22436/jnsa.013.03.01
Publication Date: November 13, 2019 Submission Date: September 02, 2019 Revision Date: September 28, 2019 Accteptance Date: October 04, 2019


T. M. M. Sow - Department of Mathematics, Gaston Berger University, Saint Louis, Senegal.


In this paper, a new iterative algorithm for finding a common element of the set of minimizers of a convex function, the set of solutions of variational inequality problem, the set of solutions of equilibrium problems and the set of fixed points of demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. Furthermore, a numerical example is given to demonstrate the implementability of our algorithm. Our theorems are significant improvements in several important recent results.