Sales of cell phones around the world rebounded in the fourth quarter, indicating that the recession may be over for the beleaguered mobile handset market, according to figures compiled by market research firms.

Global handset shipments were up 10 percent to 324.4 million units in the fourth quarter of 2009 compared to 293.8 million phones during the same quarter a year ago, said Strategy Analytics. This is the first quarter of growth the industry has seen since the third quarter in 2008.

Other research groups have also observed similar trends. ABI Research said it saw mobile handset shipments in the fourth quarter of 2009 grow about 15 percent compared to the third quarter of 2009.

But stiff competition is squeezing the average sale price of devices, which fell 2 percent to $117.55 during the fourth quarter, ABI Research said.

Nokia and Samsung Electronics each increased market share during the quarter. Nokia’s market share jumped to 37.7 percent of the market. And Samsung increased its market share to 20.5 percent.

Nokia and Samsung weren’t the only ones seeing strong growth. Other handset makers saw shipments increase. LG Electronics even broke fourth-quarter shipment records. Apple, which makes the popular iPhone, nearly doubled shipments of its smartphone compared to last…