在本文裡，我們將根據混合方法及外梯度法來引進一種新的疊代組合，並藉由此方法去尋找在希爾柏空間裡平衡系統問題的解集合、非擴張映射的固定點集合，以及單調和 k-Lipshitz 連續映射的變分不等式問題之解集合所產生的共同元素。而由此方法所疊代出的序列也產生了一些收斂性的結果。
然而，在本文裡這些結果是延伸並改進一些在文獻上已知的結果。

In this paper, we introduce a new iterative scheme based on both hybrid method and extragradient Method to find a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpansive mapping, and the solutions set of a variational inequality problems for a monotone and k-Lipschitz continuous mapping in a Hilbert space. Some convergence results for the iterative sequences generated by these processes are obtained. The results in this paper extend and improve some known results in the literature.

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