In this paper, we introduce an iterative algorithm to approximate a common solution of a generalized equilibrium problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequences generated by the iterative algorithm converge strongly to a common solution of the generalized equilibrium problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. Some applications of main results are also provided.

中文翻译：

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希尔伯特空间中渐近非膨胀映射不动点问题和广义均衡问题的通用解的近似

在本文中，我们引入了一种迭代算法来逼近真实 Hilbert 空间中渐近非膨胀映射的广义均衡问题和不动点问题的公共解。我们证明迭代算法生成的序列强烈收敛到广义均衡问题和渐近非扩展映射的不动点问题的公共解。本文中提出的结果扩展和概括了该研究领域中许多先前已知的结果。还提供了主要结果的一些应用。