I called it a fruit tree because its fruit is edible but not popular and I haven't seen it for sale in the super markets.
Its lack of popularity is probably due to that there is little to eat on it because the seeds inside are so large and the fruit meat is very dry. I liked the taste and the favour though..

On a beach;

I took a couple of the fallen fruit back home where I photographed them

The fruit and seed are much like Eriobotrya japonica, but not quite!

Pouteria is very similar, there are a lot of species in Brazil. The leaves on yours are rounded at the tip, I have found some which are like this.

http://plantillustrations.org/...

http://www.tradewindsfruit.com...

http://reflora.jbrj.gov.br/jab...

http://www.kew.org/science/tro...

Thanks Janet! It could be related to Pouteria, at least the leaves and this description of the fruit of Pouteria lucuma on 'Tradewindsfruit':

orange colored, dry pulp that is reminiscent of a hard boiled egg yolk in appearance. Flavor is very sweet, unique, and is used to flavor ice creams and beverages

fits it very well apart of course of the size and the fact that mine are grouped in neat bundles.
The fruits of mine had about a diameter of 3cm, not big at all.
I remember now someone told me that the fruit is being used to flavor ice cream!
The seeds of mine were also not in separated chambers, but 'glued' together inside the fruit, like I posted above.

24 species in the area! (Flora do Brasil), a lot but still doable..

I found out it is Mimusops coriacea! This is the only species in the area!
https://www.google.be/search?q...

Congratulations Myriam!

I see it's in the family Sapotaceae.

http://www.tropicos.org/name/2...

Thanks Janet!