Share prices suffered hefty falls on Monday, after trading in China was suspended following a 7% fall in  its main index.
The Dow Jones closed up slightly, by 10.07 points at 17,159.01. The S&P 500 index also rose, ending the day up 4.11 points at 2,016.77.
But the tech-heavy Nasdaq index fell 11.66 to 4,891.43.
Nasdaq component Apple fell 2.5% after news that it was cutting production of its iPhone 6S by 30%.
Shares of Amazon slipped 0.5%, despite it announcing a new deal with carmaker Ford that will allow Amazon users to connect technology in their vehicles with technology in their homes.
Shares in Ford fell 1.8% after the carmaker's sales for December came in slightly below forecasts.
Gunmakers were the days big climbers, despite President Obama announcing plans to increase regulation.
Smith & Wesson was up 11.8% after it predicted that earnings for the three months to 31 January would beat analysts' expectations.
(Close): Wall Street had a mixed day, following global sell-offs on Monday - the first day of 2016 trading.