In this paper, a new iterative algorithm of a Halpern-type is constructed. The sequence generated by the algorithm is proved to converge strongly to a common solution of two generalized equilibrium problems and a common J-fixed point of two continuous J-pseudo-contractive maps in a uniformly smooth and uniformly convex real Banach space. Furthermore, a numerical example is given to illustrate the implementability of our algorithm. Finally, the theorem complements, improves and unifies some related recent results in the literature.

中文翻译：

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伪压缩型图的广义均衡问题和不动点的一个通用解

本文构造了一种新的Halpern型迭代算法。证明该算法产生的序列在一个均匀光滑且均匀凸的实Banach空间中强烈收敛于两个广义平衡问题的一个公共解和两个连续J伪压缩图的一个公共J固定点。此外，给出了一个数值示例来说明我们算法的可实现性。最后，该定理补充，改进和统一了文献中一些相关的最新成果。