Abstract

In this paper, we study the variational inclusion problem which consists of finding zeros of the sum of a single and multivalued mappings in real Hilbert spaces. Motivated by the viscosity approximation, projection and contraction and inertial forward–backward splitting methods, we introduce two new forward–backward splitting methods for solving this variational inclusion. We present weak and strong convergence theorems for the proposed methods under suitable conditions. Our work generalize and extend some related results in the literature. Several numerical examples illustrate the potential applicability of the methods and comparisons with related methods emphasize it further.