A stock analyst says the string of shootings is not likely to affect the company financially.
The company says it s cooperating fully with police. And Denny's will continue its 24-7 service while it redoubles efforts to keep its restaurants safe, reports CBS News correspondent Teri Okita.
But the South Carolina-based company has struggled with its corporate image for years. Some observers say any negative news could leave a bad taste in the mouths of potential customers.
Stock analyst Mark Smith with Sidoti and Company says the shootings have no real link to the company and so should have no effects on its bottom line.
The latest shooting occurred about 2:45 a.m. at a Denny's restaurant near Angel Stadium baseball park after a fight broke out between two large groups of people in the restaurant, said Sgt. Rick Martinez of the Anaheim Police Department.
One victim re-entered the restaurant after being shot and died inside, Martinez said. The other victim was taken to a nearby hospital and is expected to survive.
A gun was found near the scene, but officers were not sure if it was the weapon used in the shooting. It appears that the shooting was not related to street gangs, Martinez said.
The gunman was being sought by authorities.
The shooting is the third to occur in a Southern California Denny's in the past three days, after unrelated incidents in Pismo Beach and Ontario.
In Wednesday, a transient with two guns walked into the restaurant at lunchtime, reportedly looking dazed, shot two men dead, wounded a husband and wife, and committed suicide.
The gunman, holding a semiautomatic handgun in one hand and a revolver in the other, entered the restaurant Wednesday and began shooting within a few steps of the front door, sending patrons and workers fleeing to the restaurant's bathrooms and kitchen, CBS News correspondent Hattie Kauffman reports. As many as 15 people were inside the restaurant at the time, authorities said.
The dead were identified as Frank Velasquez, 65, of Oceano, who was killed in front of his wife and 5-year-old great-granddaughter, and Harold Hatley, 73, of Grover Beach.
"They were just enjoying an innocent meal," Police Chief Joe Cortez said of the victims.
The gunman, identified as 60-year-old Lawrence Edward Woods, also wounded a married couple before fatally shooting himself in the head, police said.
A 37-year-old Pomona man was fatally shot in the parking lot of a Denny's restaurant in Ontario on Thursday after getting into an altercation with a group of people. The gunman was still being sought.
Denny's said Wednesday it was cooperating with police.
"We are shocked and saddened by this tragic incident," the Spartanburg, S.C.,-based restaurant chain said in a statement. "This appears to be a random act of violence."