What are some important mathematics results that were first developed in Economics? Economics is known to import mathematical methods that were proven to be useful in other areas.

There is any important result in mathematics that was first developed in the context of Economics research and then explored in other applied fields such as Physics or Engineering?
The Envelope theorem is arguably one, https://en.wikipedia.org/wiki/Envelope_theorem . I would say Blackwell's papers on comparisons of experiments are a significant mathematical contribution--extending Hardy,Littlewood and Polya's earlier results, and paving the way for further investigation.

Econometricians have made statistical contributions as well; see e.g. https://en.wikipedia.org/wiki/Heckman_correction .

More recently, I saw a paper presented last year on how a certain type of stochastic PDE could be solved by reinterpreting it as a (stochastic) differential game. I would expect to see more related to this (the relationship between differential games and stochastic pdes) in the coming years, especially given the recent surge of interest in mean-field games.