In this study, we introduce a method for finding common fixed points of a finite family of $(\eta _{i}, k_{i})$ -enriched strictly pseudocontractive (ESPC) maps and $(\eta _{i}, \beta _{i})$ -enriched strictly pseudononspreading (ESPN) maps in the setting of real Hilbert spaces. Further, we prove the strong convergence theorem of the proposed method under mild conditions on the control parameters. Our main results are also applied in proving strong convergence theorems for $\eta _{i}$ -enriched nonexpansive, strongly inverse monotone, and strictly pseudononspreading maps. Some nontrivial examples are given, and the results obtained extend, improve, and generalize several well-known results in the current literature.

中文翻译：

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涉及丰富的严格伪收缩和伪非扩展映射的有限族的定点结果

在本研究中，我们介绍了一种查找 $(\eta _{i}, k_{i})$ 有限族的公共不动点的方法 - 丰富的严格伪收缩 (ESPC) 映射和 $(\eta _{i} , \beta _{i})$ - 在真实希尔伯特空间的设置中丰富了严格的伪非扩散（ESPN）映射。进一步证明了该方法在控制参数温和条件下的强收敛定理。我们的主要结果还应用于证明 $\eta _{i}$ 丰富的非扩张、强逆单调和严格伪非扩散映射的强收敛定理。给出了一些重要的例子，所获得的结果扩展、改进和概括了当前文献中的几个众所周知的结果。