Reminds me of Runge-Kutta methods[1] of numerical integration, specifically RK2 since they only have one intermediary update.

The theorems took me right back to my finite element methods class at university, with Banach spaces and proving convergence of fixed point functions using Cauchy sequences.

Hopefully someone more well-versed in the field can chime in on the meat of the paper, looks like a good win from afar.

[1]: https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods