Let the VI indicate a variational inclusion, the CFPP denote a common fixed point problem of countably many nonexpansive mappings, and the SVI represent a system of variational inequalities. We introduce a composite viscosity implicit method for solving the VI and CFPP with the SVI constraint in the framework of uniformly convex and q-uniformly smooth Banach space where $1<q\le 2$. Moreover, we prove the strong convergence of the sequences generated by the proposed implicit method to a solution of a certain hierarchical variational inequality (HVI). In addition, our results are also applied for solving the fixed point problem (FPP) of nonexpansive mapping, variational inequality problem, convex minimization problem and split feasibility problem in Hilbert spaces.

令 VI 表示变分包含，CFPP 表示可数个非膨胀映射的公共不动点问题，SVI 表示变分不等式系统。我们引入了一种复合粘性隐式方法，用于在一致凸和q -一致光滑 Banach 空间的框架内求解具有 SVI 约束的 VI 和 CFPP，其中$\mathrm{1个}<q\le \mathrm{2个}$. 此外，我们证明了所提出的隐式方法生成的序列对某个层次变分不等式 (HVI) 的解的强收敛性。此外，我们的结果还应用于解决非膨胀映射的不动点问题（FPP）、变分不等式问题、凸最小化问题和希尔伯特空间中的分裂可行性问题。