might i ask for what purpose you want to display two hdmi signals on one monitor in split screen? that sounds a bit of an oddity, dual screens might be better as they do not distort content.
what you are looking for is often called a "multi viewer" although it could also be called a "hdmi processor/scaler" by a few companies. while some accept hdmi (the expensive ones) some also take SDI (which apparently some sdi are capable of upto 4k resolutions and have hdmi->sdi converters available) perhaps worth looking on google using those search terms.
some are capable of many display formats including side by side while some are not. i havent found anything reasonably priced though. its almost cheaper to buy another monitor or tv and use them side by side.
if you can live without hdmi and use old rca instead then i found you some products for reasonable prices and exactly what you are looking for in terms of options.