An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore, the theorem is applied to convex optimization problems and to J-fixed point problems. Finally, some numerical examples are presented to show the effect of the inertial term in the convergence of the sequence of the algorithm.

中文翻译：

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混合惯性算法在应用中逼近凸型可行性问题

研究了一种惯性迭代算法，用于逼近最大单调算子的零集中的点，该点也是可数相对非扩张算子族的公共不动点。在一致凸和一致光滑的实Banach空间中证明了强收敛定理。该定理扩展，概括和补充了一些近期的重要成果。此外，该定理适用于凸优化问题和J不动点问题。最后，给出了一些数值例子来说明惯性项对算法序列收敛的影响。