Is it permissible to announce in the mosque about lost children or lost items?

It is not permissible to announce lost property or stray animals in mosques, due to the prohibition of the Prophet (peace and blessings be upon him) against it. As for a lost child, it is permissible to call out for them in the mosque, because a child is not considered a stray animal, and preserving lives is among the objectives of Islamic law.