Britain's Heather Watson crashed out of the Japan Open in the opening round in Osaka.
Laura Robson went down 6-1 6-2 to Angelique Kerber as she was knocked out of the China Open at the second round.
Laura Robson beat Klara Zakopalova 7-6 (7-3) 4-6 6-1 to reach round two of the China Open.
Former Wimbledon champion Petra Kvitova stormed into the final of the New Haven Open, where she will face Simona Halep.
Organisers have announced the seedings for the US Open and Roger Federer is seeded only seventh.
Round-up: Samantha Stosur continued her build-up to the US Open with a convincing 6-1 7-5 win over Svetlana Kuznetsova.
Round-up: Serena Williams made a successful return to hard courts with a 6-3 6-2 thrashing of Francesca Schiavone in Toronto.
Round-up: Laura Robson withdrew from the WTA Toronto event, moments before she was to go on court to face Yanina Wickmayer.
Serena Williams defeated Klara Zakopalova 6-0 6-4 to book her spot in the final of WTA Bastad.
Serena Williams enjoyed a comfortable afternoon on her first WTA appearance since Wimbledon on the red clay of Bastad.
Round-up: Serena Williams continued her march to a Wimbledon title defence with a 6-2 6-0 win over Kimiko Date-Krumm.
Round-up: Serena Williams eased into the third round with a 6-3 6-2 win over Caroline Garcia.
Laura Robson opened her Wimbledon campaign with a convincing 6-3 6-4 win over Maria Kirilenko.
Round-up: Serena Williams began the defence of her Wimbledon title with a comfortable 6-1 6-3 victory over Luxembourg's Mandy Minella.
Twice grand slam champion Svetlana Kuznetsova pulled out of Wimbledon on Wednesday with an abdominal strain.
ATP World Tour Finals
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