For a mistake I deleted some files from my camera Sony Model DCR-SX50E. Can I recover them ?

You may try some recovery software to rescue the files on your recorder, here are some for your option.

Photo Video Music Recovery (for Windows)
Photo Video Music Recovery for Mac

Both programs can also recover video and music files.

Note: Before your files are recovered, do not attempt to save more files to the handy cam in case the original files(your recordings) are overwritten.

That depends on what have you don to this camera sin then!
In fact, the deletion process often cannot completely wipe the saved data off from the camera. These precious files are still there as long as you've not save anything new on this camera to overwrite these original files since then. So, you should take care not to save anything new there, if you still want to restore them all back.
But, right now, no matter whether you've rewritten them or not, you could apply a camera data recovery freeware to restore your deleted files back for free .
I believe this freeware would work perfectly on your camera in the same way as it successfully restores the inaccessible files back from a memory card of my friend.
You should give it a shot here:
http://blog4mark.blogspot.com/2012/12/deleted-files-recovery.html

Next time, I hope you could pay much attention to your files as you decide to delete something important.