could anyone suggest me a problem book that comprise interesting problems on topics like series , sequence , functional identities. a good problem book on real analysis is what I'm looking for.
I recommend Problems in Mathematical Analysis I, II and III by W. J. Kaczor and M. T. Nowak.
Other good book is Problems in mathematical analysis: B. P Demidovich.
And try to start solving problems from Bartle's book: Introduction to Real Analysis and Mathematical Analysis by Tom Apostol.