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• Osaka pulls out of home Japan Open through injury

  Naomi Osaka will not play at her home Japan Open next week due to a back injury, organisers confirmed on Monday.

  The 26-year-old was forced to retire during the last 16 against eventual champion Coco Gauff at the China Open in Beijing last week because of the same injury.

  Osaka was on a three-match winning streak before her meeting with Gauff, having also registered her first comeback victory in two years earlier in the tournament when she beat Yulia Putintseva in the second round.

  However, the four-time grand slam winner has not recovered in time and will not be able to play on home soil when the tournament starts on October 14.

  "Due to injury, Naomi Osaka has decided to withdraw from the tournament," the Japan Tennis Association said in a statement.

  Osaka is still scheduled to play in the Pan Pacific Open Tennis Tournament 2024 in Tokyo, which begins on October 21.

  Her last appearance in her home country was at that tournament in 2022, when she withdrew in the second-round match with abdominal pains. 

• Gauff took a relaxed approach in China Open final

  Coco Gauff said her China Open triumph over Karolina Muchova came down to being relaxed.

  Gauff won 6-1 6-3 in just 76 minutes in Beijing to become the youngest winner of the tournament in 14 years.

  The victory marked the 20-year-old's second WTA 1000 title, which makes her the second-youngest player since the format was introduced to win her first two finals.

  And Gauff explained she took a more relaxed approach in Sunday's showdown.

  "I was just like, 'This match is not going to change my life.' I knew regardless of the result today, I was proud. I was able to overcome and still work on things that I've been practising on, too, and stick to it," she said.

  "When you get that far, you're just happy to be in the final. I think it's just being relaxed. My first final, when I was 15, was the worst because you're like, 'I'm never going to get this opportunity again,' which is completely not true.

  "The experience of winning in the past, I realise that, yes, winning is great. It feels great right now. But tomorrow I'm going to wake up and it's a different day, 70% of the world doesn't know anything about whether I won or lost, probably even more."

  Gauff has now claimed three straight wins over Muchova, who is yet to beat the American.

  "I lost to her three times in a row. I'll say very similar losses. It was always the latest rounds of the tournaments when I got many matches under the belt," said Muchova.

  "It's very physical with her. I felt like second [best] always in the rallies."

• Alcaraz passes stern Wu test to progress in Shanghai

  Carlos Alcaraz held his nerve against a spirited Wu Yibing to progress to the fourth round of the Shanghai Masters.

  Having already beaten another of the home favourites, Shang Juncheng, in his opener, the Spaniard had to dig deep but prevailed 7-6 (7-5) 6-3 in one hour and 41 minutes on Sunday.

  There was nothing to split the two in the opening set, though Wu caused some real problems with his power, and successfully defended two break points in the ninth game.

  The tie-break was also tight, but Alcaraz found his edge at the right time, winning the last three points.

  Buoyed by the home crowd, Wu started the second set strongly too, but Alcaraz absorbed the pressure well and got the only break of the match in a three-game winning run.

  With his winning streak extended, Alcaraz will now face either Gael Monfils or Ugo Humbert in the next round.

  Data Debrief: Alcaraz marches on

  Alcaraz has put his shock US Open exit firmly behind him, with this his 11th win on the bounce since then. 

  He coped well with the early pressure Wu threw at him, and put in another solid performance, hitting 11 aces and winning 71% of his points at the net (5/7).