An inertial subgradient extragradient algorithm for modified variational inclusion problem and mixed equilibrium problem in real Hilbert space

Our main focus of this study is based on modified variational inclusion problems with mixed equilibrium problems in real Hilbert space. An iterative algorithm which is the combination of inertial technique and subgradient extragradient algorithm is presented, and under some reasonable assumptions on the control parameters, the strong convergence theorem of the suggested algorithm is proved. In addition, the efficiency of our suggested algorithm is established by a numerical example. The algorithm and analysis provided in this paper are new and generalize some related results in this regard.