Second seed Caroline Wozniacki rallied from a set down to beat qualifier Jarmila Gajdosova and reach the quarterfinals of the Pan Pacific Open.
Sixth-seeded Dominika Cibulkova beat Kirsten Flipkens of Belgium 6-1, 6-3 to advance to the second round of the Pan Pacific Open on Tuesday.
Top-seeded Sabine Lisicki of Germany advanced to the semifinals of the Hong Kong Open with a 6-4, 6-3 victory over China's Zheng Saisai on Friday.
Alison van Uytvanck of Belgium advanced to the quarterfinals of the Hong Kong Open by beating second-seeded Daniela Hantuchova of Slovakia 3-6, 6-2, 6-4 Thursday.
Top-seeded Sabine Lisicki of Germany advanced to the quarterfinals of the Hong Kong Open by beating Grace Min of the United States 6-1, 6-1 Tuesday.
A day after beating Venus Williams in singles at the US Open, Sara Errani and her partner, Roberta Vinci, were knocked out in the second round as the top-seeded team in women's doubles.
Taylor Townsend, Grace Min, Nicole Gibbs and Danielle Collins are among eight players receiving wild-card invitations for the U.S. Open women's draw.
Fifth-seeded Angelique Kerber of Germany beat Dominika Cibulkova of Slovakia 7-6 (5), 7-5 on Monday to move into the second round of the Sydney International, one of the last warmup tournaments for the Australian Open starting next week.
Wild card entrants Jarmila Gajdosova and Matthew Ebden combined to win the Australian Open mixed doubles title with a 6-3, 7-5 win over Lucie Hradecka and Frantisek Cermak on Sunday.
Eighth-seeded Sloane Stephens advanced to the Hobart International semifinals Thursday with a 6-3, 4-6, 7-5 win over fellow American and qualifier Lauren Davis.
Australian wild card and former champion Jarmila Gajdosova beat Olga Govortsova of Belarus 6-3, 6-1 to advance to the Hobart International quarterfinals Wednesday.
Serena Williams joked that since the calendar still read 2012, she needed to maintain this year's dominant form.
Urszula Radwanska of Poland and two other seeded players advanced to the second round of the Tashkent Open on Monday.
Canada's Aleksandra Wozniak beat fifth-seeded Klara Zakopalova of the Czech Republic 6-0, 7-6 (2) on Sunday in the first round of the Texas Open.
U.S. Olympian Christina McHale saved a set point, then used a late service break to pull out a 7-6 (5), 7-5 win over Jarmila Gajdosova in the first-round of the Mercury Insurance Open on Tuesday.
Coco Vandeweghe turned a second chance into a second-round match at the Bank of the West Classic on Monday.