Let H be a real Hilbert space. Let $F:H\rightarrow 2^{H}$ and $K:H\rightarrow 2^{H}$ be two maximal monotone and bounded operators. Suppose the Hammerstein inclusion $0\in u+KFu$ has a solution. We construct an inertial-type algorithm and show its strong convergence to a solution of the inclusion. As far as we know, this is the first inertial-type algorithm for Hammerstein inclusions in Hilbert spaces. We also give numerical examples to compare the new algorithm with some existing ones in the literature.

中文翻译：

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Hilbert空间中Hammerstein积分夹杂物解的一种惯性类型算法

令H为真实的希尔伯特空间。设$ F：H \ rightarrow 2 ^ {H} $和$ K：H \ rightarrow 2 ^ {H} $为两个最大单调和有界算子。假设在u + KFu $中包含Hammerstein包含$ 0 \有一个解决方案。我们构造了一个惯性型算法，并证明了其对包含解的强收敛性。据我们所知，这是希尔伯特空间中Hammerstein包含的第一个惯性类型算法。我们还给出了数值示例，以将新算法与文献中已有的算法进行比较。