American teenager Coco Gauff showed why she deserves to be at this year's WTA Finals with a commanding 6-0 6-3 victory over Martina Trevisan at the Guadalajara Open.

The fifth seed clinched her maiden spot at the season-ending WTA Finals on Wednesday and backed that up by securing her third WTA 1000 quarter-final on Thursday.

Gauff reeled off the first nine games of the match against Trevisan, where she triumphed in one hour and one minute. The 18-year-old came under pressure from Trevisan, who generated nine break points for the match but Gauff saved all bar one of them.

World number one Iga Swiatek (47) is the only player to have won more matches this year in straight sets than Gauff (32).

Gauff will face Victoria Azarenka in the quarter-finals after the Belarusian toppled 13th seed Madison Keys 6-4 6-7 (4-7) 6-1 in two hours and 13 minutes.

Two-time Australian Open winner Azarenka swept aside Keys in 32 minutes in the third set after a titanic battle in the opening two frames, winning 26 of the 37 final-set points. Azarenka's quarter-final appearance is her 34th since 2009, with only four players having more during the span; Agnieszka Radwanska (42), Simona Halep (39) and Caroline Wozniacki (36).

Third seed Jessica Pegula advanced to the last eight with a 6-4 6-4 victory over former US Open champion Bianca Andreescu. 

The American, who survived three match points against Elena Rybakina on Wednesday, trailed early against the Canadian but took control of the match. Pegula will face Sloane Stephens in the quarter-finals after she toppled 2022 US Open semi-finalist Caroline Garcia 7-6 (8-6) 7-5.

On the day her WTA Finals berth was confirmed, seventh seed Daria Kasatkina lost 6-2 2-6 6-3 to Anna Kalinskaya in two hours and 14 minutes.

Fourth seed Maria Sakkari fought back to win 5-7 6-3 6-3 over 14th seed Danielle Collins, while Marie Bouzkova copped a bagel before triumphing 0-6 7-5 6-3 over Liudmila Samsonova.

Sakkari will next meet eighth seed Veronika Kudermetova who beat Jelena Ostapenko 6-4 6-4. Bouzkova will take on Kalinskaya in the last eight.

Dominic Thiem saw off Francisco Cerundolo for the second time in the space of a week as he dug deep in the deciding set to win 6-1 1-6 7-5 at the European Open.

The Austrian downed the Argentinian in straight sets six days earlier in Gijon but found this a sterner test of his capabilities against the sixth seed.

Nevertheless, the former US Open winner shook off a second-set collapse and then responded to going a break down in the decider, winning four of the final five games to seal a quarter-final clash with favourite Hubert Hurkacz.

He was joined in the last-eight by two more unseeded players, as David Goffin and Sebastian Korda recorded straight-set upsets over third seed Diego Schwartzman and fourth-ranked Karen Khachanov respectively.

At the Stockholm Open, fifth seed Alex de Minaur made swift work of American J.J. Wolf, dispatching him in a 6-4 6-2 win to set up a quarter-final with Canada's Denis Shapovalov.

Defending champion Tommy Paul is out however, losing to Sweden's Mikael Ymer, who recorded a 6-2 6-3 victory that earns him a clash with top seed Stefanos Tsitsipas.

Slippery court conditions contributed to a backlog in fixtures at the Napoli Cup, meaning first-round matches were followed by second-round encounters on Thursday.

Nevertheless, second seed Matteo Berrettini made light work of Roberto Carballes Baena, winning 6-4 6-2.

Roberto Bautista Agut, seeded third, slipped to a 6-4 6-4 loss to Mackenzie McDonald, with the American joining Berrettini in the last eight.

Serena Williams says the chances of her returning to the court are "very high", despite declaring her intention to step away from tennis before the US Open last month.

Though she deliberately avoided saying she would retire prior to the tournament, instead saying she planned to "evolve" away from the sport, many believed Williams' third-round exit at Flushing Meadows last month was the last time she would be seen playing competitive tennis.

Her defeat to Ajla Tomljanovic was met with the kind of fanfare that suggested she was calling it a day on an illustrious career that included 23 grand slam titles, the second most in history behind Margaret Court.

But Williams implied she could yet step on the court again when speaking at a TechCrunch Disrupt event in San Francisco on Wednesday.

In quotes collected by the San Francisco Standard, Williams said: "I am not retired.

"The chances [of me returning] are very high. You can come to my house and [see] I have a court."

It was a great day for the highly ranked Americans at the Guadalajara Open on Wednesday, headlined by world number five Jessica Pegula and her 2-6 6-3 7-6 (10-8) comeback win over Wimbledon champion Elena Rybakina.

Pegula, who is now locked into the top-eight and therefore will qualify for the WTA Finals, struggled to win points on her serve in the opening set, but raised her 57 per cent success rate up to 69 per cent in the second set, and 66 per cent in the decider.

The American had to come from a break down in the second set to keep her tournament alive, and she will now face Canada's Bianca Andreescu in the third round.

Meanwhile, fellow United States star Coco Gauff was too good for Italy's Elisabetta Cocciaretto, winning 7-6 (7-1) 6-3 to book a third-round clash with another Italian, Martina Trevisan, who earned her way there with a 6-0 4-6 6-3 win over Katerina Siniakova.

The other two seeded Americans were also successful, with 13th seed Madison Keys coming from a set down to defeat Ajla Tomljanovic 3-6 6-4 6-3, and 14th seed Danielle Collins repelled the challenge of Magdalena Frech 6-3 6-4.

There were positive signs for former world number five Eugenie Bouchard, who ended up losing, but showed she still has her talent by taking a set off world number 23 Jelena Ostapenko in a 7-5 2-6 6-1 result.

Russian pair Anna Kalinskaya and Liudmila Samsonova both emerged in three-set outings, with Kalinskaya outlasting Elise Mertens 6-4 0-6 7-5, while Samsonova upset world number four Aryna Sabalenka 6-4 2-6 6-2.

World number 12 Veronika Kudermetova kept her WTA Finals hopes alive with a 6-4 7-5 win over Donna Vekic, and the Czech Republic's Marie Bouzkova ousted Colombia's Camila Osorio 6-3 6-1.

In the late window, Sloane Stephens eliminated Olympic gold medalist Belinda Bencic 6-4 6-4, and top overall seed Paula Badosa retired due to injury after losing the first set 6-2 against Victoria Azarenka.

Cameron Norrie fought back from a first-set loss against Aslan Karatsev to advance into the quarter-finals of the Stockholm Open, keeping hopes of qualifying for next month's ATP finals alive.

Norrie's return to action, having withdrawn from last month's Korea Open with illness, was not plain sailing as Karatsev won the first set tie-break 10-8 to put the Brit under pressure.

However, the 27-year-old responded by taking the next two sets 6-3 6-4 to seal safe passage, helped by six first-serve aces, which also maintains his hopes of a spot in November's finals and sets up a tie against 19-year-old Holger Rune.

Top seed Stefanos Tsitsipas was given a sterner test by Maxime Cressy before eventually securing a spot in the quarter-finals 7-6 (7-5) 7-6 (14-12) in a two-hour contest, while Denis Shapovalov also beat Antoine Bellier in straight sets.

The number one seed is through at the European Open in Antwerp as well as Hubert Hurkacz toppled Jack Draper 7-6 (7-5) 6-7 (5-7) 6-1.

Britain's Dan Evans eased into the final eight after securing a 6-2 6-1 victory against Constant Lestienne, while there were also victories for Yoshihito Nishioka and Richard Gasquet.

Elsewhere, sixth-seed Sebastian Baez was a 7-5 7-6 (7-3) winner against Lorenzo Sonego in the Napoli Open, where Roberto Carballes Baena and Corentin Moutet were among the other victors.

The top seed in action on Tuesday at the Guadalajara Open made it through her opening match unscathed as Maria Sakkari defeated Marta Kostyuk 6-4 6-4.

Sakkari is one of the players needing a strong result in the tournament to break into the top-eight of the world rankings to qualify for the upcoming WTA Finals, entering the week at 10th, but only needing to make up one spot, with number eight Simona Halep out due to injury.

With her victory over Kostyuk, Sakkari avoided notching four consecutive losses for the first time this season, and will likely only need one more win to move into WTA Finals contention.

Her next opponent appears to be world number 16 Danielle Collins, who had no issue dispatching American compatriot Caroline Dolehide 6-4 6-1 to book her second-round fixture against Magdalena Frech after the Polish qualifier beat Yulia Putintseva 6-3 6-4.

World number seven Daria Kasatkina also should be locked into the WTA Finals after cruising past China's Lin Zhu 6-1 6-2, while 18th-ranked Beatriz Haddad Maia's season is over after a disappointing 7-5 6-2 upset loss to Katerina Siniakova.

Petra Kvitova needed to reach the final to have a chance of qualifying, but after a strong first set she fell 3-6 6-2 6-0 against Canada's Bianca Andreescu. In a good day for the Canadians, Eugenie Bouchard also beat Kayla Day 7-5 6-3 as the former world number five fights her way back up the rankings after a long injury layoff.

Italy's Elisabetta Cocciaretto defeated Russia's Anastasia Potapova 6-2 6-1, while Latvia's top talent Jelena Ostapenko cruised past America's Lauren Davis 6-1 6-3.

Madison Keys was too strong for Magda Linette in a 6-3 6-3 triumph, and in an all-Czech matchup, Marie Bouzkova downed Tereza Martincova 6-2 7-5.

Croatia's Donna Vekic eliminated Brazil's Laura Pigossi 6-4 6-1, and Italy's Martina Trevisan showed why she is top-30 in the world with a convincing 6-4 6-3 straight sets win against Japan's Nao Hibino.

In the last match of the night, world number 10 Caroline Garcia survived an early scared to come from behind and defeat Rebecca Marino 6-7 (2-7) 6-3 7-6 (7-5).

Grigor Dimitrov crashed out of the Stockholm Open to the unseeded Jiri Lehecka in a three-set thriller on Tuesday, as Botic van de Zandschulp also fell at the first hurdle at the European Open.

Dimitrov, seeded sixth in the Swedish capital, came up short against Lehecka, who seized a surprise 6-4 1-6 7-6 (7-5) win, his first on the ATP Tour since July.

Victory for Alex de Minaur was far more predictable, a 150th at tour level coming courtesy of a straight-sets defeat of Benjamin Bonzi.

In Antwerp, Dominic Stricker handed Van de Zandschulp a swift exit, winning 6-2 6-4 to stay on Lehecka's coat tails in pursuit of a place at the Next Gen ATP Finals.

Stricker's reward for this win will be a second-round encounter with French veteran Richard Gasquet, who knocked out three-time grand slam champion Stan Wawrinka on Monday.

At the Napoli Cup, fifth seed Miomir Kecmanovic saw off wildcard Flavio Cobolli with ease, but others found life rather tougher.

Respective seventh and eighth seeds Albert Ramos-Vinolas and Adrian Mannarino fell to Nuno Borges and Pedro Cachin.

Victoria Azarenka has booked a clash with the top seed of the Guadalajara Open after defeating Elina Avanesyan 6-4 6-2 in Monday's opening round.

In the last event of the season before the WTA Finals, Belarus' Azarenka was too strong with her return game for her Russian opponent, winning 53 per cent (32-of-60) of her return points while capitalising on five-of-seven break point opportunities to earn a shot at world number eight Paula Badosa.

While Azarenka has no chance of qualifying for the WTA Finals – with only the top-eight players in the rankings making it through – Belinda Bencic is one of the players who can sneak in with a great result this week.

Needing to make the semi-finals to have a chance, she got off on the right foot with a 7-5 6-7 (10-12) 6-3 win against Leylah Fernandez in her opening match.

Petra Kvitova can also qualify if she reaches the final, and she started without issue, defeating Bernarda Pera 6-3 7-5.

Ekaterina Alexandrova had an outside chance of claiming a WTA Finals spot if she won this tournament, but she was the victim of the day's biggest upset, falling 6-4 7-6 (10-8) to Camila Osorio.

At 22nd in the world, Liudmila Samsonova is the lowest-ranked player in the field with a mathematical chance at qualification, but she is a step closer after handling Kaia Kanepi 6-1 7-5.

Despite Fernandez's earlier loss, it was a strong day for the Canadians, with Bianca Andreescu proving too good in her 6-2 6-4 victory against Jil Teichmann, and Rebecca Marino also only needed two sets to defeat Ann Li 6-2 7-6 (7-2).

China's Lin Zhu came from a set behind to beat France's Alize Cornet 3-6 6-3 6-4, while Ukraine's Marta Kostyuk had a much quicker result in her 6-1 6-3 triumph over Belarus' Aliaksandra Sasnovich.

World number 34 Elise Mertens had no problems in one of the biggest mismatches of the day as she defeated world number 185 Asia Muhammad 6-3 6-2, and Sloane Stephens needed only 54 minutes to advance 6-0 6-2 past Linda Fruhvirtova.

In the last match of the night, Mexico's top chance Fernanda Contreras Gomez was eliminated by Alja Tomljanovic 6-2 6-1.

Holger Rune maintained his impressive form by beating Thiago Monteiro in straight sets to reach the second round of the Stockholm Open on Monday.

Rune was beaten by Marc-Andrea Huesler in the final of the last tournament he entered in Sofia following a quarter-final appearance in Metz.

The Danish teenager, who last week announced Patrick Mouratoglou had joined his team for the rest of this season, defeated Monteiro 7-5 6-2 on his debut in the Swedish capital.

Rune did not face a break point and won 86 per cent of points on his first serve as he booked a meeting with Cristian Garin.

Garin beat qualifier Jason Kubler 6-2 6-4, while Maxime Cressy and Aslan Karatsev advanced to the last 16 at the expense of Ilya Ivashka and Lukas Rosol respectively.

Richard Gasquet consigned Stan Wawrinka to an early exit at the European Open, coming from a set down to win 2-6 7-6 (7-4) 6-4 in a battle of two of the most experienced players on the circuit.

Fifth seed Dan Evans beat Tallon Griekspoor 6-3 6-4 in the first round in Antwerp, while his fellow Brit Jack Draper was an emphatic 6-1 6-2 winner against Jenson Brooksby of the United States.

Iga Swiatek says she "wanted to go all in" to ensure she won her eighth WTA Tour title of 2022 with a 6-3 3-6 6-0 victory over Donna Vekic in the San Diego Open final on Sunday.

Swiatek became the fifth player since 2000 to win eight or more WTA-level titles in a single season after Martina Hingis, Serena Williams, Kim Clijsters and Justine Henin.

She did not have it all her own way against Vekic, with the Croatian world number 47 battling back from losing the opener to take the second set and level the match.

But Swiatek showed her class in the decisive third set, breaking Vekic three times to romp to the title.

The world number one says she had to give it everything to ensure victory over Vekic in a tough match, saying at her on-court presentation: "It was a really tight match and pretty long.

"We felt the intensity for sure. At the end I wanted to be the one who played the last ball in. I wanted to go all in.

"Knowing how well she can serve, I just wanted to be more loosened up on my return games - not think too much, use my intuition and fight for every ball."

With her round-of-16 win over Zheng Qinwen, Swiatek became the first player to win 61 matches in a single season since Caroline Wozniacki in 2017.

Frighteningly for her opponents, the 21-year-old spoke after that win of her belief that she was still a few years away from her prime.

"I wasn't expecting to have this kind of season this year," Swiatek told reporters. 

"I thought, maybe, I'm going to be at my peak when I'm 24, 25, and have that experience, maybe results like that are going to come."

Swiatek's 64 wins in 2022 is the most for any woman since Serena Williams' 78 in 2013, while the Pole has lost just one match in the United States this year.

Swiatek intends to take full advantage of San Diego's sun and sand as she celebrates another title, making it 11 wins and just two defeats in finals.

"I am speechless," the 21-year-old said in a video on Twitter. "I'm so proud of me and the team that we actually won this tournament.

"It wasn't easy so I'm happy that I believe in myself and I fought to the last point.

"I love San Diego, I'm going to enjoy the beach tomorrow!"

World number one Iga Swiatek claimed her eighth WTA Tour title of the season, storming home to claim a three-set victory over Donna Vekic in the San Diego Open final on Sunday.

Swiatek improved her record in the United States to 24-1 this season with the victory in one hour and 47 minutes, getting past the Croatian qualifier 6-3 3-6 6-0.

The Pole previously won the US Open, along with the Indian Wells and Miami titles this season.

Top seed Swiatek secured her 64th win of the season, which is the most since Serena Williams won 78 in 2013.

Vekic ensured it was not easy for Swiatek, continuing her excellent week – knocking out Maria Sakkari, Karolina Pliskova, Aryna Sabalenka and Danielle Collins - with a strong second set.

The Croatian actually had to complete her semi-final earlier on Sunday after a rain-interrupted encounter with Collins, winning 6-4 4-6 7-6 (7-2) after resuming 4-2 down in the third set, before taking on Swiatek.

Swiatek's dominance was felt, winning 82 per cent of her second-serve points, ruthlessly converting four of six break points as well.

Vekic only generated one break point for the match but she took it, keeping the match alive in the second set where she was more aggressive.

The 2022 US Open and French Open champion responded emphatically in the final frame, capitalising on three of four break points and winning 24 of the 29 points for the set to triumph.

J.J. Wolf was no match for Felix Auger-Aliassime in the final of the Firenze Open, as the Canadian won 6-4 6-4 in Florence.

Auger-Aliassime is targeting a place in the end-of-season ATP Finals and took a huge step towards securing such a spot on Sunday.

The top-seeded 22-year-old only dropped one set throughout the tournament and has now won his second ATP Tour-level title.

His victory over Wolf, the world number 75 who will rise to 56 on Monday, took only one hour and 41 minutes.

"It never gets old. Winning, it always feels like the first time," Auger-Aliassime, the new world number 10, said in his on-court interview.

"It's so special to win, especially here. I had a fantastic week and it's been amazing.

"Every final is tough, it's the two best players of the week. Of course you try to win more than you lose the finals, and that's why I came out here today ready to give everything.

"We had some very tough rallies in the second set, feeling tough physically. But you keep pushing, try to keep the level high.

"But there's no magic. Sometimes you win, sometimes you lose, but of course I'm really happy because I came here [as] the first seed.

"I was the favourite in all of my matches on paper. It's never an easy position, so to come out and win my four matches with confidence and conviction, it's really good for my confidence."

Wolf saved nine of the 12 break points he offered yet could not make any inroads against Auger-Aliassime's serve, with the champion winning without conceding on his service game.

Qualifier Anna Blinkova landed the first WTA singles title of her career by beating Jasmine Paolini in Sunday's Transylvania Open final.

The 24-year-old world number 138 had to come through qualifying in Cluj-Napoca, and she completed a stellar campaign at the Romanian event by getting her hands on the trophy.

Blinkova won 6-2 3-6 6-2 in an hour and 41 minutes, scotching Paolini's hopes of a second title in her tour career.

"I felt great the whole 10 days that I spent here since last Wednesday," the Russian said in her trophy acceptance speech. "I'm really looking forward to coming back next year."

The WTA said Blinkova's success made her the fifth qualifier to secure a tour title in 2022, following victories for Tatjana Maria in Bogota, Anastasia Potapova in Istanbul, Bernarda Pera in Budapest and Caroline Garcia in Cincinnati.

Blinkova, who was once ranked 54th in the world, will return to the world's top 100 on Monday.

Andrey Rublev defeated Sebastian Korda in straight sets in Sunday's Gijon Open final to land his 12th ATP Tour title.

The Russian had already prevailed in Belgrade, Dubai and Marseille this year and added another crown to his collection with a 6-2 6-3 victory against Korda in 75 minutes.

Top seed Rublev had dropped only one set in his three matches en route to the final and impressed against Korda with 29 winners, three breaks and just four unforced errors.

Korda, seeking a second Tour-level trophy following success in Parma last year, had his serve broken in the fourth and eighth games of the opening set.

Some heavy-hitting exchanges kept spectators gripped, though Rublev proved too strong for Korda in the second set and earned the only break in the sixth game.

Rublev got over the line with his fourth match point and remains sixth in the chase for an ATP Finals spot, with four of those ahead of him already qualified, along with Novak Djokovic. 

World number one Iga Swiatek qualified for her ninth WTA Tour of the year, coming from a set down to get past fourth seed Jessica Pegula at the San Diego Open on a rain-affected Saturday.

Swiatek was at her dominant best against Pegula after dropping the opening frame, breaking her opponents' serve four times in the latter two sets to triumph 4-6 6-2 6-2 in two hours and six minutes.

The Pole extended her domination of Pegula this year, winning all four of their encounters in 2022, while the victory is her 63rd of the season, equaling Angelique Kerber's mark from 2016. Swiatek is also 23-1 in the United States this season.

Swiatek finished with 22-8 forehand winners, while she won 75 per cent of her second serves, compared to Pegula's 38 per cent.

After Pegula won the first set that included three breaks of serve, the match was halted for more than an hour due to rain, with Swiatek revealing post-game she passed time with crosswords.

That worked for the top seed who raced to a 3-0 second-set lead after the resumption and did not drop serve for the remainder of the match, saving three break points at 2-2 in the third.

The 2022 French Open and US Open champion will take on either Croatian qualifier Donna Vekic or American world number 19 Danielle Collins in Sunday's decider after their semi-final was ultimately suspended due to rain.

Collins leads Vekic 4-6 6-4 4-2 with the match restarted three times after rain, before the call was made to postpone it until Sunday, no earlier than 12.30pm local time, with the final to be played later in the day.