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Sania will compete alongside Kazakhstan's Anna Danilina at the Australian Open, which begins on January 16, before bidding farewell to the sport in the UAE.
Martina said her prognosis is good and she will start treatment this month.
Greek fourth seed Sakkari kept alive her hopes of making the Finals by surviving an early scare and fighting back from a set down to beat American Danielle Collins 5-7, 6-3, 6-3.
The women's doubles pair of Treesa Jolly and Gayatri Gopichand also made a winning start.
Chloe Kelly scored the late winner as England women clinched their first major title.
Sania had earlier announced that she would hang up her racquet at the end of this season.
The second seed Spaniard won 6-4 6-4 4-6 6-3 in his second round match against Lithuania's Ricardas Berankis.
The Spaniard beat Francisco Cerundolo 6-4 6-3 3-6 6-4 in the first round.
World No. 1 Swiatek crushed her Russian opponent 6-2, 6-1 while teenager Gauff recorded a comfortable 6-3, 6-1 win over Trevisan in the semifinals.
Trevisan had all the answers as she dominated most of the match against a below-par Fernandez who struggled to repeat the form that took her to last year's US Open final.