August 11, 1983

The nation's rental car industry, benefiting from an upturn in air travel and an increase in demand for the used cars it sells to the public, is apparently recovering after two stagnant years. The turnaround was reflected this week in the announcement by the RCA Corporation, owner of the Hertz Corporation, that it was ending its 18- month effort to sell the nation's largest rental car company. ''We began seeing an upturn in January, and I expect the business to continue getting better throughout the year,'' said Frank A. Olson, the Hertz chairman, in an interview yesterday. Hertz has about 38 percent of the rental car market.

New York City yesterday pulled out of an agreement with the state's Urban Development Corporation to redevelop Times Square and said it would complete the $1 billion plan itself. Mayor Koch announced the withdrawal in a statement read by the chairman of the City Planning Commission, Herbert J. Sturz, at a board meeting of the Times Square Redevelopment Corporation. The Times Square agency is made up of two members appointed by the city, including Mr. Sturz, and three by the U.D.C., including its chairman and president, William J. Stern.

Because of an editing error, an article yesterday about the decision of the A.F.L.-C.I.O. executive council to advance the date of the labor federation's Presidential endorsement incorrectly described the procedure. The federation's general board is to recommend a candidate to the convention.

THE heart starts to pound, the upper lip trembles, the mouth dries out, the eyes blur, the butterflies start fluttering in the stomach. Many people know the meaning of these symptoms: It is time to give a public speech. Until recently, it was usually men who suffered in this manner. But now that more women have jobs that frequently require them to do public speaking, they, too, are having to cope with the stage fright and nerves that have made it so feared. Speech experts often quote a survey taken in 1973, in which 3,000 Americans were asked: ''What are you most afraid of?'' Their most frequent reply: ''Speaking before a group.'' It was mentioned more often than death, illness and financial problems. According to the experts, the fear of being humiliated and the fear that others will ''see the real person underneath'' are the major causes of difficulty.

A raging underground electrical fire in midtown Manhattan yesterday plunged the garment center and the city's busy Herald Square commercial district into a chaotic, extended power failure. The blackout struck an area of 12 square blocks - from 30th to 42d Street between the Avenue of the Americas and Seventh Avenue. It closed hundreds of offices and businesses, including Macy's and Gimbels, clogged traffic in much of midtown, knocked out thousands of telephones and disrupted countless lives. At 5:37 P.M., 16 hours after flames erupted in a subterranean power station that had been flooded by a water-main break, firefighters brought the blaze under control. Major Losses Feared But officials of the Consolidated Edison Company said heavy damage to electrical equipment in the fire-ravaged vault under Seventh Avenue and 38th Street made it unlikely that all power would be restored to the area before Monday. Efforts to make emergency hookups to three other power substations in Manhattan were expected to begin today.