Convergence Properties and Numerical Illustration of a Resolvent-Based Inertial Extrapolation Method for Variational Inclusions in Banach Space

This paper examines H(·,·)-accretive mappings in Banach spaces and proves that the resolvent operator related to these mappings is Lipschitz continuous. Using the resolvent operator technique, we formulate iterative algorithms to solve a class of variational inclusions in Banach spaces. We also concentrate on examining the convergence of the problem by employing the inertial extrapolation scheme and proving the convergence of the iterative scheme produced by the algorithm. The theoretical analysis is corroborated with a numerical result, which highlights the effectiveness and practical relevance of the proposed approaches.