Regarding similarity index of research mathematics papers, I would like to know what is the acceptable similarity index for journals in average?
I am assuming you mean a turn-it-in type similarity index. There is no acceptable similarity index. Even a 1% similarity index could be the result of an entire paragraph being the same in a long paper. That is not acceptable. It could also just be random matches and not an indication of plagiarism. Even a similarity index of zero is suspicious since it would be surprising for sequence of words to match in a paper and therefore suggests the authors may have intentionally hid something. In other words, algorithmic detection of plagiarism still needs a human to look at it. At the upper limit, a similarity index in excess of 50% is almost always indicative of something wrong.
The key is that plagiarism and copying other people's ideas is not allowed regardless of what the similarity index is.