This manuscript deals with two problems: the first one is a variational inclusion problem involving an m-accretive mapping and a finite family of inverse strongly accretive mappings, and the other one is a fixed point problem having an infinite family of strict pseudo-contraction mappings in Banach spaces. To approximate the common solution of these problems, we design a generalized viscosity implicit iterative scheme with Meir–Keeler contraction. A strong convergence result for the proposed iterative scheme is established. Applications based on convex minimization problem, linear inverse problem, variational inequality problem and equilibrium problem are derived from the main result. The numerical applicability of the main result and some applications are demonstrated by three examples. Our result extends, generalizes and unifies the previously known results given in literature.

中文翻译：

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通过包括应用在内的广义粘度隐式方案来解决一个有限类的夹杂问题和一个无限点的定点问题

该手稿涉及两个问题：第一个是涉及m的变分包含问题。-增生映射和有限的逆强增生映射族，另一个是在Banach空间中具有无限族的严格伪收缩映射的不动点问题。为了近似解决这些问题的通用解决方案，我们设计了具有Meir–Keeler收缩的广义粘度隐式迭代方案。建立了该迭代方案的强收敛结果。从主要结果得出了基于凸极小化问题，线性逆问题，变分不等式问题和平衡问题的应用。通过三个例子证明了主要结果的数值适用性和一些应用。我们的结果扩展，归纳和统一了文献中已知的结果。