Apple analysts are sticking by their predictions for the company’s fourth-quarter prospects as the tech giant’s stock struggles to recover from a painful slide.

Apple stock opened below $500 for the second day in a row Wednesday, still feeling the fallout from weekend reports that it had cut orders for iPhone screens. The company’s 52-week low is $488.27; its stock was trading just above $500 in mid-morning trading.

Reports from Japan’s Nikkei service and the Wall Street Journal indicated that Apple had almost halved an order for 4-inch screens, a key component in its latest phone, as well as other phone components. Both based their reports on unnamed sources in Apple’s supplier chain. The Nikkei report referred specifically to orders at Sharp and Japan Display, Inc.

Those reports, however, are the subject of some dispute, and analysts have been standing their ground on their forecasts.

In a note to investors, Sterne Agee analyst Shaw Wu said that he’s confident that demand for the iPhone 5 remains the same, despite what he calls “great confusion” over press reports about weak demand. Wu said he attributes the reports of screen order cuts to better production yields (meaning Apple has to order fewer screens) and supplier shifts.

Some are challenging the reports over the sheer number of screens that they say Apple ordered for the upcoming quarter — historically one of the weakest quarters for smartphone demand.

On Monday, Boy Genius Report’s Tero Kuittinen called the numbers in the Nikkei report “strange math.” Kuittinen said that the original order figure of 65 million screens far outstrips even the most optimistic iPhone estimates for next quarter.

“In what world did Apple expect to order components for 65 million iPhone 5 handsets in the seasonally soft March quarter?” Kuittinen wrote.

All of this discussion puts additional pressure on the Cupertino, Calif., company as it prepares to to release its own all-important sales and revenue figures on Jan. 23. Apple will have to show a strong holiday quarter to calm its investors, particularly as its competitors report their own milestones.

The company’s largest rival, Samsung, reported Monday that it has sold 100 million Galaxy S phones, 40 million units of the Galaxy S III alone. Nokia reported surprisingly good (though not iPhone competitive) sales figures of its Windows Phone-base Lumia 920, indicating there may be a stronger appetite out there for a non-Apple, non-Android phone than analysts think.

Related stories:

Bloomberg: Apple iPhone suppliers decline on report orders cut by 50%

Bloomberg: Apple iPhone needs to adapt to emerging-market growth, Sculley says

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