Naomi Osaka stumbled badly in her first match since winning the Australian Open as the world number one went down in a flurry of errors to exit the Dubai Championships on Tuesday.Dubai-based Frenchwoman Kristina Mladenovic claimed a 6-3, 6-3 victory to reach the third round as Osaka made 25 unforced errors.The rout, which featured seven breaks of the Osaka serve, took barely an hour, sending Mladenovic into a Wednesday contest with Carla Suarez Navarro.This is my home tournament, I live here, world number 67 Mladenovic said. Its great to get a win like this in front of a big crowd.Beating the number one is always special.The second set was riddled with seven consecutive breaks of serve before Mladenovic finished off the job with a winner to the empty court on match point.Osaka stunned the tennis world last week by announcing her split from coach Sascha Bajin despite winning back-to-back Grand Slam titles at the US and Australian Opens.She said earlier this week that she would not prioritise success over happiness when asked about the sacking, and she never looked like winning in Dubai as she also served five double faults.Earlier on Tuesday, Simona Halep and Petra Kvitova both won their opening matches, while Elina Svitolina made a strong start to her bid for a third straight title.Kvitova, the 2013 winner, recovered from losing a first-set tiebreak to defeat Katerina Siniakova 6-7 (37), 6-4, 6-4 and squeeze into the third round.Halep, Dubai champion in 2015, saw off 2014 Wimbledon finalist Eugenie Bouchard 7-6 (74), 6-4.The Romanian said she is still feeling the effects of her weekend final defeat in Doha by Elise Mertens.It was a good match because I won it. I tried to finish the points faster because Im a little bit tired, Halep said.She played well, the level was pretty good. At some points I really ran very well. Im confident. I feel good on court even if Im tired.A third former world number one also advanced as Angelique Kerber beat Dalila Jakupovic 7-6 (74), 6-3.Kvitova, Wimbledon champion in 2011 and 2014, said she was unfazed about the early midday start to her match.I dont really care if I play the first match, the Australian Open runner-up said. Now Im done, so I have a free afternoon.Im not sure what Im pleased with... maybe with my comeback at the end.Svitolina benefits from Jabeur injuryLocal favourite Ons Jabeur was forced to retire with the Tunisian trailing Svitolina 7-6 (74), 4-0.Jabeur took a fall late in the opening set, rolling her ankle while also hitting her shoulder.She took a medical timeout out but was only able to carry on in the second set for four games.Third seed Svitolina is hoping to become the first women to win three Dubai titles.That is a big motivation for me here, the Ukrainian said. Today I didnt really feel in a match mood, I dont know why. I was struggling a bit, I had a very slow start. Hopefully tomorrow will be better.I told myself that Im here to make history of the tournament.Elsewhere, Hsieh Su-Wei defeated Belarusian Aliaksandra Sasnovich 6-1, 6-2 while Viktoria Kuzmova accounted for seventh seed Kiki Bertens, beating this months St Petersburg champion 6-2, 4-6, 7-6 (86).American Jennifer Brady downed French 14th seed Caroline Garcia 6-4, 7-5 as her compatriot Sofia Kenin defeated Russian 11th seed Daria Kasatkina 6-3, 2-6, 6-4.A third US player, Alison Riske, advanced 6-2, 6-3 over Alize Cornet.