Thrinax parviflora

Thrinax parviflora Sw., Prodr. Veg. Ind. Occ. 57 1788. ; 
Florida Thatch Palm is an attractive fan palm growing up to 15 ft with a graceful slender trunk. Trunks can grow 30-40 ft tall, but are only 5 inches thick.
It develops numerous 3 ft palmate leaves which have up to 60 pleat-like segments. The segments extend two-thirds into the blade and have drooping tips. Leaves are dark green above, silvery beneath. Leaft stalks are about 3 ft long.
Flowers are borne in sprays 3-4 ft long, with many short yellowish branches bearing white bisexual flowers. Fruit is round, 1.2 cm wide, white when ripe.
This is a very slow growing pine. This palm does well in humid weather, and is native to coastal areas of the North American continent.
Araceae, Arecaceae and Zingiberaceae Fortnight :: Arecaceae :: Thrinax parviflora from Hiranandani Powai, Heritage Gardens :: ARKAUG-33 : 6 posts by 3 authors. Attachments (3).
Attached are pictures of Thrinax parviflora captured at Hiranandani Powai, Heritage Gardens in January 2013.
Requested to please validate the ID.
Yes, seems Ok
Is this a Branching Palm ? : 5 posts by 3 authors. Attachments (1)- 4 MB. 
is this a Branching Palm ?
Location -Sagar Upvan, Mumbai
Date - April. 2018

The Branching Palm that I had seen at Mazagaon Gardens in Mumbai looked different.   

I think close to images at Thrinax parviflora Sw.