The purpose of this article is to suggest a modified subgradient extragradient method that includes double inertial extrapolations and viscosity approach for finding the common solution of split equilibrium problem and fixed point problem. The strong convergence result of the suggested method is obtained under some standard assumptions on the control parameters. Our method does not require solving two strongly convex optimization problems in the feasible sets per iteration, and the step-sizes do not depend on bifunctional Lipschitz-type constants. Furthermore, unlike several methods in the literature, our method does not depend on the prior knowledge of the operator norm of the bounded linear operator. Instead, the step-sizes are self adaptively updated. We apply our method to solve split variational inequality problem. Lastly, we conduct some numerical test to compare our method with some well known methods in the literature.

本文的目的是提出一种改进的次梯度超梯度方法，包括双惯性外推法和粘度方法，用于寻找分裂平衡问题和不动点问题的共同解。该方法的强收敛结果是在控制参数的一些标准假设下获得的。我们的方法不需要在每次迭代的可行集中求解两个强凸优化问题，并且步长不依赖于双函数 Lipschitz 型常数。此外，与文献中的几种方法不同，我们的方法不依赖于有界线性算子的算子范数的先验知识。相反，步长会自适应更新。我们应用我们的方法来解决分裂变分不等式问题。最后，我们进行了一些数值测试，将我们的方法与文献中一些众所周知的方法进行比较。