Roger Federer said his grand slam revival was well underway Saturday as he smoothly reached week two at the Australian Open, but Maria Sharapova admitted she had to improve or go out. As cooler temperatures consigned this week’s heatwave to memory, Federer swept past Russia’s world number 79 Teymuraz Gabashvili 6-2, 6-2, 6-3 in what is his record 57th consecutive major tournament. Federer, with an unsurpassed 17 grand slam titles but now aged 32, last year lost in Wimbledon’s second round and in the last 16 at the US Open, raising doubt about his ability to win more major titles. But the Swiss, who said he was comfortable with his new, bigger racquet and with Swedish great Stefan Edberg in his corner, hoped his 2013 difficulties were now behind him. “It was a tough year last year and it took some time to figure out what I needed to do to feel better and to get my confidence back, because that’s what I thought it was mostly,” Federer said. “For the last four to five months I feel that I’m back to normal again and at least I feel I’ve done the work to catch up and haven’t had any setbacks, so it’s very positive.” Federer, who now faces either Jo-Wilfried Tsonga or fellow Frenchman Gilles Simon, said he was happy with his first week’s work in dismissing James Duckworth, Blaz Kavcic and now Gabashvili without losing a set. “I didn’t have the best of Wimbledon and US Opens last year, and I didn’t want to get ahead of myself,” the four-time champion said. “Now the draw is getting extremely difficult, regardless of whether it is Jo-Wilfried or Gilles, but I’m looking forward to it... I’ve done the work and haven’t lost a set so far.” Russia’s Sharapova was less impressive, and less convinced about her form, after struggling for a second successive match before ousting France’s Alize Cornet. The third seed, on her way back after a shoulder injury, was made to work for the win before coming through 6-1, 7-6 (8/6). She also had trouble putting away Italy’s Karin Knapp in the second round. “There are definitely things I’m going to have to improve and do better moving forward, because it only is going to get tougher,” she said. Sharapova will next play Slovakian seed Dominika Cibulkova, who beat Spain’s Carla Suarez Navarro. Serb Jelena Jankovic won against Kurumi Nara, her third successive Japanese opponent, to set up a meeting with Romanian Simona Halep. America’s Sloane Stephens, a semi-finalist last year, beat Ukraine’s Elina Svitolina and will next face either defending champion Victoria Azarenka or Yvonne Meusberger, who play later. France’s Stephane Robert beat Slovakia’s Martin Klizan in what was the first third-round grand slam clash between two ’lucky losers’ - who failed to come through qualifying, but earned their spots due to withdrawals - in 41 years. And in the men’s doubles, Indian-Pakistani pair Rohan Bopanna and Aisam-ul-Haq Qureshi ended the grand slam comeback of British cancer survivor Ross Hutchins and his partner, Colin Fleming.