Thrinax parviflora ?


Bangalore on 27-05-09; Palm for ID-280509-RK2 - indiant
reepix | Googl
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Fruit of Thrinax radiata - Florida Thatch Palm - 180913 - RK : Attachments (2). 3 posts by 2 authors.
Posting pics of this Palm.
In the 2nd pic the fruit can be seen faintly on the left of the palm.
Better pics - of inflorescence & the palm - appear here:  
I think similar Palms has been identified as Thrinax parviflora Sw. in the postings by Raman Arunachalam & Alka Khare (Validation by Andrew Henderson)
Are both same or different & are both being cultivated in India ?
T. parviflora has been mentioned in Floriculture in India - Page 314 as:
... T. parviflora. Another beautiful species which is a native of Jamaica, Cuba, and Florida. The petiole is reddish at the base. The leaves are 90 to 120 cm across, having ...
But I did not find any such mention of Thrinax radiata in any India books on google search.