Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space $E^{*}$ . In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational inequality problems and fixed points of a countable family of relatively nonexpansive maps. The theorems proved are improvement of the results of Censor et al. (J. Optim. Theory Appl. 148:318–335, 2011).

中文翻译：

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求解变分不等式和凸可行性问题的次梯度超梯度算法的收敛定理

令C为具有对偶空间$ E ^ {*} $的一致光滑且2一致凸的实际Banach空间E的一个非空闭合且凸的子集。在本文中，构造了Krasnoselskii型次梯度超梯度迭代算法，并将其用于逼近变分不等式问题和可数相对非膨胀图族的不动点解的一个公共元素。证明定理是对Censor等人的结果的改进。（J. Optim。Theory Appl。148：318-335，2011）。