The over-relaxed scheme based on $$H(\cdot ,\cdot )$$ H ( · , · ) -cocoercive operators for solving a generalized variational inclusion problem

Abstract

In this paper, we introduce and study an over-relaxed scheme based on \(H(\cdot ,\cdot )\)-cocoercive operators for solving a generalized variational inclusion problem in Hilbert spaces. By using the resolvent operator technique associated with \(H(\cdot ,\cdot )\)-cocoercive operators, an existence and convergence result is proved. Our over-relaxed scheme seems to be more general and applicable for solving many related problems occurring in applied sciences. An example is provided in support of our main result.