AI 中文总结
研究由不连续严格单调函数生成的广义拟算术平均的等式问题，给出两个充分条件得类似结论，举例说明无额外条件时生成函数非仿射变换，其余情况考虑函数逆得出缩放因子在连续区域一致的结论。
AI 中文摘要
我们研究了由不一定连续的严格单调生成函数$f$产生的广义拟算术平均的等式问题。我们给出了两个充分条件，得出了与帕莱斯和帕斯特茨卡结果类似的结论。通过一个例子表明，在我们的情况下，若无额外条件，不能期望生成函数在整个定义域上是彼此的仿射变换。在其余情况下，我们考虑函数的适当逆，这意味着缩放因子在各个连续区域必须一致。
英文摘要
We study the equality problem of generalized quasiarithmetic means for a strictly monotonic generator $f$ that is not necessarily continuous. We provide two sufficient conditions that lead to a conclusion analogous to the result of Páles and Pasteczka. We show through an example that in our case, without any extra conditions, the generator functions cannot be expected to be affine transformations of each other over the whole domain. In the remaining case, we consider the appropriate inverses of the functions, which implies that the scaling factor must coincide across the various regions of continuity.
