Strong convergence of a generalized forward-backward splitting method in reflexive Banach spaces

In this paper, we study the so-calledgeneralized monotone quasi-inclusion problemwhich is a generalization and extension of well-known monotone quasi-inclusion problem. We propose a forward-backward splitting method for solving this problem in the framework of reflexive Banach spaces. Based on Bregman distance function, we prove a strong convergence result of the proposed algorithm to a common zero of the problem. As an application, we apply the main result to the variational inequality problem. Finally, we provide some numerical examples to demonstrate our algorithm performance. The results presented in this paper improve and extend many known results in the literature.

Automated summary

This paper studies the generalized monotone quasi-inclusion problem and proposes a forward-backward splitting method to solve the problem. By applying the Bregman distance function, the strong convergence of the algorithm is proven and applied to the variational inequality problem. Numerical examples demonstrate the performance of the algorithm.