On some generalized split problems and their solutions

Abstract

 In this paper, we design some generalized split problems which can be seen as an extended form of the split variational inequality problems. We present several iterative algorithms for solving generalized split problems and demonstrate the weak convergence results under some appropriate assumptions within the context of real Hilbert spaces. Finally, we support these results with the help of numerical examples in both the finite and infinite dimensional spaces. As a result of this work, a new direction will be opened in studying split problems.