French Open: Novak Djokovic defeated Mikael Ymer 6-0, 6-2, 6-3 to march into the second round at Roland Garros.
Simona Halep won her first Italian Open on Monday after defeating defending champion Karolina Pliskova, who retired injured in the final.
US Open: World number one Novak Djokovic dropped the first against Britain's Kyle Edmund but rallied to progress 6-7 (5/7), 6-3, 6-4, 6-2.
Novak Djokovic and Karolina Pliskova progressed to the second round after winning their opening matches in an empty Arthur Ashe Stadium.
New York Governor Andrew Cuomo gave the green light for the US Open to be held from August 31 to September 13.
Garbine Muguruza had to struggle two days after ending the current comeback of Kim Clijsters as Spain's double grand Slam champion grappled with her world number 39 opponent.
Elina Svitolina became the latest seed in the women's draw to make an exit after being well beaten by unseeded Garbine Muguruza in the third round.
Karolina Pliskova's defeat to Anastasia Pavlyuchenkova means that two of the top three seeds are now out of the women's draw at the Australian Open.
World number two Karolina Pliskova barrelled into the Australian Open second round on Tuesday as she chases her first Grand Slam crown.
Dumped out of the Brisbane International last week, Ashleigh Barty retains a comfortable cushion of 1,607 points over Karolina Pliskova, who went on to win the Brisbane title.
Karolina Pliskova's third Brisbane International title in four years and her 16th on the WTA tour, stamps her as one of the favourites for the Australian Open.
Karolina Pliskova triumphed 6-7 (10/12), 7-6 (7/3), 6-2 in a two hour, 48 minute marathon and will play eighth seed American Madison Keys in the decider.
Karolina Pliskova has hired Venezuelan coach Daniel Vallverdu with former Ukraine Fed Cup player Olga Savchuk -- a long-time friend -- also joining her team.
Ashleigh Barty won four titles in 2019 including the prestigious WTA Finals and finished the year on top of the WTA rankings.
Ashleigh Barty, playing in her WTA Finals debut, will look to cap off a momentous season when she plays Elina Svitolina in Sunday's final.
World No.12 Sofia Kenin replaced Bianca Andreescu after the US Open champion suffered a knee injury against Karolina Pliskova on Wednesday.
WTA Finals: Simona Halep moved on top of Purple Group alongside defending champion Elina Svitolina who earlier beat No.2 seed Karolina Pliskova.
WTA Rankings: Ashleigh Barty once again retained the top spot in but will have to produce her top performance at Wuhan Open to retain her No. 1 spot.