Sania Mirza beat Crotia's Karolina Sprem 6-4, 6-2 in the first round of the US Open.
Australia's Samantha Stosur failed to allay fears she could be heading for another early exit at her home Grand Slam with a scrappy performance in Hobart while a trio of big names tumbled out of the Sydney International on Monday.
Flavia Pennetta beat unseeded Italian compatriot and childhood friend Roberta Vinci 7-6(4) 6-2 to win the US Open women's singles title on Saturday.
List of French Open women's singles champions:
Poland's world number four Agnieszka Radwanska breezed past Spaniard Larra Arruabarrena 6-0, 6-2 in the semi-finals of the Korea Open on Saturday to set up a title clash with Russia's Anastasia Pavlyuchenkova.
Djokovic is clubbed with Federer, Juan Martin Del Potro, David Goffin and Alexander Zverev.
Steady rain hit the US Open on Monday, washing out the last match on Arthur Ashe Stadium court featuring five-time champion Roger Federer.
The 30-year-old is the first German woman to win Wimbledon since Steffi Graf in 1996.
Simona Halep became the first Romanian in 40 years to lift the French Open trophy at Roland Garros on Saturday.
List of French Open women's singles champions
Images from Day 3 of the 2020 French Open at Roland Garros, in Paris, on Tuesday.
Rafael Nadal returns to his favourite tournament, albeit not his preferred court, to begin pursuit of a record-extending 10th French Open title on Monday against Frenchman Benoit Paire.
Serena Williams started her quest to join Chris Evert and Martina Navratilova in joint fourth place on the career Grand Slam list with a 6-3, 6-1 victory over 18-year-old fellow American Taylor Townsend at the US Open on Tuesday.
Factbox on Wimbledon champion Marion Bartoli, who announced her retirement from tennis at 28 after a second round loss at the Western and Southern Open in Cincinnati on Wednesday.
List of French Open women's singles champions
IMAGES of the all the action from Day 1 of the Australian Open played at Melbourne Park on Monday
Milestones in the progress of Chinese women's tennis after Li Na, the first Asian to win Grand Slam singles titles, announced her retirement from the sport on Friday.
Sam Stosur powered into the French Open quarter-finals with a 7-6(0), 6-3 win against Simona Halep in Paris on Tuesday, adapting better to damp and heavy conditions than her higher-ranked Romanian opponent.
All major sporting events in the Paris region were suspended on Saturday as France mourned the victims of the attacks in the capital city the night before that left 129 people dead and 352 wounded.
'I was trying to play every match like it was my last one. Trying to play best all the time' 'For me it is easy to practise and stay in this life but sometimes it is hard to compete'
IMAGES from matches played on Day 4 of the French Open at Roland Garros on Wednesday
Jelena Ostapenko became only the sixth female Grand Slam champion to lose in the opening round of their title defence on Sunday when she lost to Kateryna Kozlova at the French Open.
Second seed Garbine Muguruza, bidding to add the Wimbledon crown to her French Open title, was sensationally beaten in the second round on Thursday by Slovakian qualifier Jana Cepelova 6-3, 6-2 in the shock of the tournament so far.
Top seed Agnieszka Radwanska's title defence at the Sydney International lasted just 92 minutes when she was dumped out of the second round by Bethanie Mattek-Sands on Tuesday.
Angelique Kerber's first Grand Slam match since winning the Australian Open in January ended in despair after she was beaten 6-2, 3-6, 6-3 by Kiki Bertens of the Netherlands in the French Open first round in Paris, on Tuesday.
Reigning French Open champion Maria Sharapova, former world number one Venus Williams and Australian Samantha Stosur sailed into the second round of the China Open with straight set victories on Sunday.
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