The parent company of United Airlines, the UAL Corporation, yesterday reported a $537 million loss in the first quarter as a 51 percent increase in fuel costs overwhelmed efforts to raise fares at the country’s second-largest carrier, the New York Times reported today. United plans to reduce employment by 1,100 by the end of the year, as airlines begin a new round of layoffs. United increased the number of planes it plans to shed to 30, from an earlier estimate of 15 to 20, in hopes of constraining capacity and driving fares up further. JetBlue Airways and AirTran Holdings, two formerly fast-growing discount carriers, also posted first-quarter losses. JetBlue reduced its growth plans for the year, hoping to keep raising fares. AirTran said that it would delay growth plans in the 16 months beginning in September. AirTran, whose shares have fallen in the wake of bankruptcy filings by some smaller carriers, said that it would sell notes and stock to raise about $110 million and bolster its cushion against the downturn.