Simona Halep produced a strong performance to reach the third round of the US Open for the first time since 2016.
The 16th seed, who has been battling injuries for much of the summer, beat Kristina Kucova 6-3 6-1 in the opening match on Arthur Ashe Stadium.
Halep made the semi-finals in New York in 2015 but has not enjoyed much success at the tournament over the last few years.
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She faces Elena Rybakina or Caroline Garcia next.
Ons Jabeur needed just 53 minutes as she eased to a 6-0 6-1 win over Maria Camila Osorio Serrano.
The 20th seed will next face Elise Mertens after she won in straight sets against Valentini Grammatikopoulou.
Garbine Muguruza reached the third round for the first time since 2017 as she beat Andrea Petkovic in straight sets.
Two-time Grand Slam champion Muguruza won 6-4 6-2 to set up a meeting with Victoria Azarenka or Jasmine Paolini.
Fifth seed Elina Svitolina won 6-2 7-5 against Rebeka Masarova.
Osaka will face Leylah Fernandez or Kaia Kanepi in the next round
Danilovic said in a message on Instagram that her withdrawal was due to “a non-Covid related viral illness”.
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Source: Euro Sports