how to obtain accepted solution views for a particular duraion(month)

Shivshankar - There doesn't seem any API parameter for this. You could utilize the OOTB component for this. Also, check out this page which gives you the required info. 

https://community.lithium.com/t5/solutions/acceptedsolutionsleaderboardpage/node-display-id/community%3Alithosphere/timerange/one_month 

Please note, this takes into account the last 30 days, last 6 months and so on.

I hope this helps.