Second seed Agnieszka Radwanska swatted aside Russia's Nina Bratchikova to reach the second round of the US Open at Flushing Meadows.

The Pole made her first grand slam final at Wimbledon earlier this summer, losing in three sets to Serena Williams, and she was never troubled in a 6-1 6-1 victory on Arthur Ashe Stadium.

Former world number one Ana Ivanovic, seeded 12th, is also through, the Serbian beating Ukrainian qualifier Elina Svitolina 6-3 6-2 in round one. It was the end of the road, though, for 41-year-old Kimiko Date-Krumm from Japan, who continues to put aside talk of retirement but lost out 6-4 6-2 to Sweden's Sofia Arvidsson.

Radwanska retired during her first match in New Haven last week because of a right shoulder problem and wore heavy strapping.

The 23-year-old said: "I'm just very happy that I could give it my best in the first match. My shoulder feels better right now. It's always difficult. Every week it's a different surface, different balls."

Venus Williams has not been a factor at a grand slam for a long time but the American wasted little time defeating countrywoman Bethanie Mattek-Sands 6-3 6-1 on Arthur Ashe.

It was at the US Open last year that Williams revealed she was suffering from the auto-immune disease Sjogren's Syndrome and she was a shadow of her former self in losing to Elena Vesnina in the first round at Wimbledon in June.

But the 32-year-old showed promising signs at the Olympics, where she won a fourth gold medal in the doubles with sister Serena, while she reached the semi-finals in Cincinnati two weeks ago.

Two seeds were sent packing, with 24th seed Klara Zakopalova losing 6-4 6-4 to fellow Czech Andrea Hlavackova while Russia's Elena Vesnina knocked out 32nd seed Peng Shuai from China 7-6 (7/5) 6-1.