K mart Corp. reported yesterday that its third-quarter earnings declined to $77.4 million (60 cents a share) from $92.4 million (71 cents) in the third quarter of 1984, but that the latest results mark a substantial improvement from the previous quarter of this year.

Meanwhile, the rollercoaster financial ride of cable television entrepreneur Ted Turner took a new tumble in the first nine months of the year as his Turner Broadcasting System Inc. lost $5 million (23 cents a share), TBS reported yesterday in Atlanta.

With adjustments for recent acquisitions, K mart's pro forma earnings per share for last year's third quarter would have been 67 cents, Chairman Bernard M. Fauber said yesterday at the company's headquarters in Troy, Mich.

"Profits for third-quarter 1985 were down 16.1 percent from the prior year, a substantial improvement over the 48.2 percent decline reported for second-quarter 1985," Fauber said.

Sales for the latest quarter, which ended on Oct. 30, increased 4.6 percent to $5.22 billion from $4.99 billion for the same period of last year.

Sales in comparable K mart stores, open a full year, were down 3 percent from the same period of 1984.

Nine-month net income was $210.7 million ($1.64), compared with $294.8 million ($2.27) last year.

Sales rose 10.2 percent for the first three quarters of 1985 to $15.67 billion, from $14.22 billion in 1984.

Comparable K mart store sales for the first three quarters this year were up 1.4 percent from the same 39 weeks of 1984.

"Cautious consumer spending has delayed the normal pickup in holiday and winter sales," Fauber said. "However, we anticipate an improvement in the pace of sales as we get closer to Christmas."

Analysts said it was not as sharp a profit fall as expected.

Jeffrey Edelman, a retail analyst with Dean Witter Reynolds, said he doubts that K mart will benefit from a major sales pickup in the balance of the year.

"The full year will be helped by recent acquisitions, but as for a major pickup in sales -- the economy just isn't responding very quickly to permit this to happen," Edelman said.

*Third-quarter profits at Turner Broadcasting System Inc. were $2.41 million (11 cents) on revenue of $92.7 million, compared with net income of $5.29 million (26 cents) on revenue of $77.67 million for the same period of 1985.

Turner's nine-month loss came on revenue of $259.44 million and compared with 1984 nine-month net income of $8.09 million (40 cents) and revenue of $210.64 million.

Spokesman Arthur Sando attributed the earnings decline to Turner's aggressive takeover battle for CBS Inc.

That bid resulted in a lengthy legal tug of war in which CBS emerged the victor.

"Included in the results of the three months and nine months ended Sept. 30 is a $627,000 benefit and $13.10 million charge, respectively, relating to the company's withdrawn exchange offer for CBS Inc., net of gain from the sale of company-owned CBS shares and income tax benefits," Sando said.

In July, Turner attempted to gain a 67 percent interest in CBS, offering up to $175 a share for outstanding CBS stock then valued at no more than $123.50. But the price included so-called "junk bonds."

CBS circumvented the takeover by buying back 21 percent of its own stock, a move that was upheld by a federal court.

When the CBS takeover collapsed, Turner then made an offer for MGM-United Artists Inc. and, in an attempt to find the cash for that purchase, put up for sale a portion of his Cable News Network, a subsidiary of TBS.

National Broadcasting Co. and Gannett Co. Inc. are seen as likely suitors for CNN, but to date no agreement has been reached.