AN EFFICIENT ITERATIVE METHOD FOR SOLVING SPLIT VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS

A new strong convergence iterative method for solving a split vari-ational inclusion problem involving a bounded linear operator and two max-imally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibil-ity problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed meth-ods. Numerical comparisons with some existing iterative methods are also presented.