AI 中文总结
该研究针对含可数族不动点型映射、平衡双函数及单调变分不等式算子约束的公共解问题，提出Legendre–Bregman外逼近法，在无需NST相容性条件下获强收敛性，还推导了Hilbert空间等特殊情形。
AI 中文摘要
我们在一致光滑且一致凸的Banach空间中，针对公共解问题提出了Legendre–Bregman外逼近法。约束系统包含可数族的不动点型映射、平衡双函数及单调变分不等式算子。在无需族级NST相容性条件的情况下，获得了从初始点到公共解集的Bregman投影的强收敛性。局部定理涵盖负熵生成元，同时也推导了Hilbert空间与Alber泛函情形。
英文摘要
We develop a Legendre--Bregman outer-approximation method for a common-solution problem in a uniformly smooth and uniformly convex Banach space. The constraint system consists of countable families of fixed-point-type mappings, equilibrium bifunctions, and monotone variational-inequality operators. Strong convergence to the Bregman projection of the initial point onto the common solution set is obtained without a family-level NST compatibility condition. A localized theorem covers negative-entropy generators, and Hilbert-space and Alber-functional cases are also derived.
