In solving the split variational inequality problems in real Hilbert spaces, the co-coercive assumption of the underlying operators is usually required and this may limit its usefulness in many applications. To have these operators freed from the usual and restrictive co-coercive assumption, we propose a method for solving the split variational inequality problem in two real Hilbert spaces without the co-coerciveness assumption on the operators. We prove that the proposed method converges strongly to a solution of the problem and give some numerical illustrations of it in comparison with other methods in the literature to support our strong convergence result.

在求解实际希尔伯特空间中的分裂变分不等式问题时，通常需要底层算子的强制性假设，这可能会限制其在许多应用中的用途。为了使这些算子摆脱通常和限制性的矫顽力假设，我们提出了一种在两个实数希尔伯特空间中求解分裂变分不等式问题的方法，而没有算子上的矫顽力假设。我们证明了所提出的方法可以很强地收敛到问题的解决方案，并且与文献中的其他方法相比，可以给出一些数值说明，以支持我们的强收敛性结果。