なんか after て- form of a verb?

Question

I am confused by the use of `なんか`, especially after the て-form of a verb. What do: `あきらめてなんかない`, `消えてなんかない` mean? How do they differ from simply saying `あきらめていない`, `消えていない`?　What is the purpose of `なんか`？

Answer 1

In the pattern NANKA...NAI, although its a negation, it implies the speaker's derogatory, humble or unexpected feeling toward the thing/event/state expressed.

あきらめてなんかない - there's no giving up vs. あきらめていない - hasn't given up

消えてなんかない - there's no erasing it vs. 消えていない - hasn't disappeared