In a -uniformly convex and uniformly smooth Banach space , the CFPP and VIP are utilized to indicate a common fixed-point problem and a variational inequality problem, respectively. We devise and discuss triple-adaptive projection method with inertial effect for resolving bilevel split VIP (BSVIP) with CFPP constraint of finite Bregman relatively demicontractive mappings in . The method exploits the strong pseudocontractivity of one mapping at the upper-level VIP and the pseudomonotonicity of another mapping at the lower-level SVIP. We establish the strong convergence outcome for the proposed method under certain suitable restrictions on the algorithm parameters without the prior knowledge of the operator norm or the coefficient of the underlying operator. In the end, an illustrated instance is invoked to bear up the practicability and performability of the proposed method.

中文翻译：

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Banach空间中有限Bregman相对半收缩CFPP约束的双层分裂变分不等式的三重自适应投影方法


在均匀凸且均匀光滑的Banach空间 中，CFPP和VIP分别用于表示常见的不动点问题和变分不等式问题。我们设计并讨论了具有惯性效应的三重自适应投影方法，用于求解具有有限 Bregman 相对半收缩映射的 CFPP 约束的双层分割 VIP (BSVIP)。该方法利用了上层 VIP 的一个映射的强伪收缩性和下层 SVIP 的另一映射的伪单调性。我们在算法参数的某些适当限制下为所提出的方法建立了强收敛结果，而无需先验算子范数或基础算子的系数。最后通过一个实例来验证该方法的实用性和可执行性。