(CNN) Serena Williams' claims of sexism after her US Open final defeat by Naomi Osaka earlier this month have divided opinion on the women's WTA Tour.

World No 1 Simona Halep and two-time Wimbledon champion Petra Kvitova told CNN Sport they have seen no difference in the way male umpires treat players, irrespective of their gender.

But Australian Open champion Caroline Wozniacki believes her long-time friend "has a point."

Japan's Osaka won the September 8 final 6-2, 6-4 after a match which saw Williams warned for coaching, penalized a point for smashing her racket and then docked a game for an outburst in which she called the umpire, Carlos Ramos, a "thief" and a "liar."

The American, who told Ramos she "never cheated" and "would rather lose" than be coached, later accused the Portuguese of sexism, saying several male players had behaved and said much worse but not been punished as harshly.

However, Halep came to the defense of Ramos, saying he had acted correctly.

"The rules are the rules," Halep, this year's French Open winner, told CNN Sport in an interview in Wuhan, China. "I don't see any difference between the men's rules and women's rules, and I think the chair umpires are doing just their jobs."

As for Ramos, Halep said: "I never had any problems with him, or with any umpire. I also got fines, when I had to. It's normal."

'No difference'

Kvitova and French No. 1 Caroline Garcia also told CNN Sport they had not experienced any differential treatment.

"I don't see the difference, to be honest," said Kvitova, who was surprised someone as experienced as Williams had reacted so strongly to the coaching violation.

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"Sometimes, when you get the violation, it is just a violation, and it is nothing, at the end of the day," said the fifth-ranked Czech. "I got so many violations when I was a kid, I got a coaching violation as well, but it's OK.

"You get it, and you can't do anything with it, and sometimes it's tough, but you can't get interrupted by that."

Garcia, the French No 1, agreed. "I think umpires treat women and men the same way, from my own experience. I think if a player got angry and reacted like she did in the final, they would get the same penalty, I am pretty sure."

'Serena has a point'

World No 2 Wozniacki said she understood where Williams, a long-time friend, was coming from.

"I think she has a point in some of what she's saying," Wozniacki told reporters in Wuhan. "I think everyone has the right to their own opinion.

"I think that when you're going into a grand slam final, you're fighting for your 24th slam, you're fighting to be on paper, the best player to ever have played the game ... there will be emotions involved. I think there will be some feelings there when you go onto the court."

Petra Kvitova told CNN Sport that Serena Williams had overreacted to the umpire's decision.

And Wozniacki said she felt Ramos should have shown more consideration for the situation.

"If someone knows Serena, if someone has followed her career, she never gets coaching, and she never asks for the coach on court," said the Dane.

"I think as a great umpire -- you obviously have to be a good umpire to be in the finals -- you should also be aware that this is the situation. You should be aware that Serena is not one of those people that really looks up to the box or communicates with the box.

"In my opinion I think that in the situation he probably should have given her a soft warning, and if he felt this is the way it was, said that your team is making signs, you need to make them stop. That's, in my opinion, the way that the umpires usually do it."

Wozniacki also said the rules should be tightened up to reduce the room for controversy.

"I think there should be some strict rules," she said. "I think those rules are kind of a gray zone. I think every match should be the same.

"If you were to be strict ... then you should have taken both players and the coaches before the match and said, Hey, I'm really strict today. I tolerate nothing. It's the way it is. That's also OK."

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Former US Open finalist Madison Keys said she believed Williams "felt like (it was) a very personal attack."

And the American said she felt the tennis authorities needed to learn from the incident.

"We can maybe look at past things and see how other situations were handled, specifically in the US Open, which kind of raises some eyebrows," Keys said.

"I think overall it was just a really unfortunate experience. I think we should probably look at it more closely and see if there is a bigger issue. If there is, it's something that needs to be addressed."

Everyone agreed, though, that the incident had spoiled Osaka's joy at becoming a grand slam champion, especially when the crowd began booing (toward officials) during the trophy ceremony.

"It's been a bit sad for Naomi actually," Kvitova said. "She played great, and unfortunately the crowd just didn't give her the best of what she deserved."

Keys also said Osaka deserved better.

"The first words out of her mouth after she won her first Grand Slam were, I'm sorry. I felt so bad. I mean, it was just really sad watching it all unfold."

Photos: Naomi Osaka: US Open champion's career in pictures - After turning professional in September 2013, Osaka made her WTA main-draw debut at the 2014 Bank of the West Classic. The then 16-year-old showed her promise by defeating former grand slam champion Samantha Stosur in her opening match. The eventual winner of that tournament? Serena Williams. Hide Caption 1 of 8 Photos: Naomi Osaka: US Open champion's career in pictures - Fast forward a year and the young Japanese player was beginning to work her way up the world rankings. She ended 2015 by winning the 2015 Rising Stars Invitational exhibition, defeating Caroline Garcia in the final. Hide Caption 2 of 8 Photos: Naomi Osaka: US Open champion's career in pictures - Osaka reached her first grand slam at the 2016 Australian Open. The 18-year-old qualifier progressed to the the third round, before being roundly beaten by eventual winner Victoria Azarenka. Osaka went on to reach the third round at both Rolland Garros and the US Open later that year. Hide Caption 3 of 8 Photos: Naomi Osaka: US Open champion's career in pictures - Osaka finished 2016 by reaching her first WTA final. After being handed a wildcard to compete at the Toray Pan Pacific Open, the youngster (left) finished runner-up behind Caroline Wozniacki (right). The successful year yielded rich rewards for Osaka. She broke into the world Top 50, signed a worldwide marketing agreement and was voted newcomer of the year at the WTA Awards. Hide Caption 4 of 8 Photos: Naomi Osaka: US Open champion's career in pictures - Osaka built on her breakthrough 2016 by playing in all four grand slams in 2017. Performing consistently on the biggest stage enabled the youngster to test herself against the world elite. Perhaps her most notable victory came in the first round of the 2017 US Open. Osaka defeated defending champion Angelique Kerber in straight sets, before being knocked out in the third round. Hide Caption 5 of 8 Photos: Naomi Osaka: US Open champion's career in pictures - After achieving her best grand slam finish at the 2018 Australian Open (fourth round), Osaka won her first WTA title at the 2018 BNP Paribas Open, Indian Wells. She cemented herself as a future star with wins against former world No.1's Maria Sharapova and Simona Halep on her way to victory. Hide Caption 6 of 8 Photos: Naomi Osaka: US Open champion's career in pictures - In March 2018, Osaka was pitted against her tennis hero for the first time, in the first round of the Miami Open. It was Serena's fourth comeback match since giving birth and Osaka ran away with a comfortable straight sets victory. Hide Caption 7 of 8 Photos: Naomi Osaka: US Open champion's career in pictures - The pair then met for a second time, at the 2018 US Open final. Serena was aiming for her 24th Grand Slam title and Osaka was competing in her first grand slam final. Amid controversy involving her opponent and the umpire, the 20-year-old Japanese star deservedly won in straight sets for her biggest career win to date, earning $3.8 million in the process. Hide Caption 8 of 8

On Sunday, Williams reflected on the incident with Ramos in an interview with Australia's Channel Ten, saying that female players could not get away with "even half of what a guy can do."

"Right now we are not, as it's proven, in that same position," said Serena.

"But that's neither here nor there. I'm just trying most of all to recover from that and move on."