Is there any Open Source GIS Software for Android in which we can perform Various Geoprocessing Operations (like buffering, union and intersection) and that should be customizable e.g.: what we do in QGIS which is Desktop Based.
[GIS] Developing GIS Application on Android
androidopen-source-gissoftware-recommendations
Best Answer
There was a QGIS Android project as part of this year's Google Summer of Code. Marco Bernasocchi was the author, and although it is largely a work in progress, he has managed to get the basics working on an Android tablet. Just search QGIS Android and you'll come up with several links to mailing list posts, his blog, and download links.
For a proper useable GIS with groprocessing, this is your best (rather, only) option, but it is in the very early stages so you will have to wait until Marco gets more time/funding, or someone carries on development.