I want to init a Map and want to always put the same BigDecimal value from outside of the stream.
BigDeci
The second argument (like the first one) of toMap(keyMapper, valueMapper) is a function that takes the stream element and returns the value of the map.
In this case, you want to ignore it so you can have:
set.stream().collect(Collectors.toMap(Function.identity(), e -> samePrice));
Note that your second attempt wouldn't work for the same reason.