A unified scheme for solving split inclusions with applications

Abstract

In this article, we propose an iterative scheme for solving a generalized split common null point problem. The iterative method uses self‐adaptive stepsizes that do not depend on the Lipschitz constants of the underlying operators. Instead, the stepsizes are updated using a simple updating formula. We prove the strong convergence theorems of the sequence generated by the iterative scheme under some mild assumptions. Furthermore, we derive iterative methods for solving split generalized variational inequality, convex feasibility, and minimization problems. In addition, some numerical illustrations are provided to support the main result.