We first introduce the weighted averaged projection sequence in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces and then we establish some inequalities for the weighted averaged projection sequence. Using the inequalities, we prove the asymptotic regularity and the $\unicode[STIX]{x1D6E5}$-convergence of the weighted averaged projection sequence. Furthermore, we prove the strong convergence of the sequence under certain regularity or compactness conditions on $\text{CAT}(\unicode[STIX]{x1D705})$ spaces.

中文翻译：

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-空间加权平均投影的收敛

我们首先介绍加权平均投影序列$\text{CAT}(\unicode[STIX]{x1D705})$空间，然后我们为加权平均投影序列建立一些不等式。利用不等式，我们证明了渐近正则性和$\unicode[STIX]{x1D6E5}$-加权平均投影序列的收敛。此外，我们证明了序列在一定规律性或紧致性条件下的强收敛性$\text{CAT}(\unicode[STIX]{x1D705})$空格。