The unprecedented explosion of takeover activity in the broadcasting and publishing industry continued today as two media giants, Cox Communications Inc. and Multimedia Inc., each received buyout bids of more than $1 billion.

Cox Enterprises, the Atlanta-based publisher of 21 daily newspapers including The Atlanta Journal and The Atlanta Constitution, offered $75 a share, or about $1.16 billion, for all Cox Communications shares that are not already owned by the Cox family.

The family owns about 55 percent of the company's shares, which after the announcement of the buyout bid soared $14.25 to $76.50 and was one of the most active issues on the New York Stock Exchange. Because the stock price jumped above the Cox bid, analysts speculated that a higher bid might be forthcoming.

Only days after published reports that former Treasury secretary William Simon was backing Cable News Network founder Ted Turner in a hostile takeover bid for CBS Inc., Simon's name surfaced again in the offer for Multimedia.

He reportedly offered about $1 billion for Multimedia Inc., a South Carolina company that owns newspapers, radio and television stations and other media operations. Multimedia's directors late last week rejected a proposal reported to have been made through a New Jersey-based investment banking firm called Wesray Corp., which Simon controls. The company declined to identify who made the bid and Simon was not available for comment.

Multimedia then approved a sweetened management buyout proposal, which analysts said was roughly equivalent to the outside offer. The offer of $41.25 in cash and $26.54 in debt per share is subject to approval by the company's stockholders. The management buyout would allow some Multimedia shareholders to retain an interest in the company, but would greatly reduce the public investment.

The company said it rejected the outside offer because it was contingent upon the sale of significant assets, including the company's newspaper operations.

Multimedia is a Greenville, S.C.-based communications company that publishes 13 daily and 30 non-daily newspapers, owns five television and 12 radio stations, operates 100 cable franchises and syndicates and produces television programs, including "The Phil Donahue Show."

Cox Communications has been mentioned as a likely takeover target since the announcement by Capital Cities Communications Inc. on March 18 that it has agreed to acquire American Broadcasting Companies Inc. for more than $3.5 billion.. Cox, which had revenue of $742 million and net income of $87 million in 1984, owns seven television stations and 12 radio stations. It operated cable television systems that serve about 1.5 million customers, many of them in Virginia.

Cox Enterprises, which is owned by Barbara Cox Anthony of Honolulu and Anne Cox Chambers of Atlanta, said it expects routine approval of the deal by the Federal Communications Commission. Cox Communications has scheduled a directors meeting to vote on the offer this Thursday.

Wall Street analysts expect the deal to be approved on Thursday, creating an Atlanta-based giant with combined 1984 revenue exceeding $1.3 billion. The merger would protect Cox Communications from a hostile takeover bid by an unfriendly raider, assuring the Cox family's continued control of media properties including television stations in Atlanta, Pittsburgh and Charlotte.

Cox Communications was founded in 1934 by Ohio Gov. James M. Cox, who bought a radio station in Dayton.

Cox stock traded between $40.50 and $55.25 last year, so the offer represented a significant premium to the company's recent stock price.