Indianapolis-based Republic Airways Holdings Inc. and its Frontier Airlines unit filed a trademark-infringement case against the operator of a website offering gift cards as consumer incentives.

The carriers on Dec. 1 sued World Avenue USA LLC of Sunrise, Fla., three other named defendants and 10 unnamed defendants in federal court in Denver. The website makes unauthorized use of the Frontier trademarks in its offerings of free gift cards, the airline said in its court papers.

World didn’t respond immediately to an e-mail requesting comment.

According to an exhibit filed with the complaint, World Avenue had previously been the target of a consumer-protection suit filed in Florida state court in August 2007 by the state’s attorney general.

Both suits relate to pop-up windows that promise free merchandise in return for meeting certain requirements, typically filling out questionnaires and surveys. Republic alleges that World Avenue has been offering Frontier Airlines gift cards without authorization as incentives.

On its website, World Avenue says it has previously been investigated by the attorneys general of Florida and Texas. The Florida investigation closed in January 2008, and the attorney general’s suit was dismissed. World Avenue said in a statement at that time that the suit related to its use of “Free” in Internet ads, and that the attorney general “made no determination that the company had violated any law, rules or regulations.”

World Avenue said it made a $1 million contribution to the Florida Department of Legal Affairs’ Revolving Trust Fund “to assist with future efforts in developing industrywide standards and best practices.” It also said it voluntarily agreed “to make certain changes to minimize the potential for any possible misunderstanding by consumers.”

World said in a May 2008 statement that there had been “no determination that the company had violated any law, rules or regulations” in the investigation by the Texas attorney general.

World said that “in its bid always to be a responsible corporate citizen,” it agreed to reimburse the attorney general’s office for its investigation expenses.

Republic also named as defendants World Chairman Niuniu Ji and Online Reward Center, a name under which it said World does business.

Republic asked the court to order the defendants to quit using any of the Frontier marks without authorization, and for monetary damages, attorney fees and litigation costs. The airline also asked that damages be tripled and that profits relative to the alleged infringement also be awarded.