But for Cook and his executives the mutterings are growing louder before the Worldwide Developers Conference that Apple just isn't innovating any more, since the death in October 2011 of Steve Jobs, its co-founder and Cook's predecessor.

To counter that, Cook and his team are expected to announce a "smart home" initiative, whereby an iPhone or iPad will be able to interact with lighting controls, heating systems, air conditioners and appliances, as well as "Health Book" software for future versions of the iPhone that will gather personal health data - perhaps through some sort of unrevealed wearable technology.

But critics say Cook's team still has big questions to answer.

Where, for example, are mobile payments to compete with Google Wallet, so its 800 million iTunes account holders can pay for things with their iPhones?

Where is a smart watch, when Samsung has released two versions since September, while Google is pushing its "Android Wear" software?

Instead, critics argue, Apple has its US$3 billion purchase of Beats - which makes headphones and offers music streaming, both of which Apple does already. "It makes no sense," wrote analyst Pascal-Emmanuel Gobry. "This deal stinks, but more importantly it reveals that Apple as we've known and loved it is gone - forever."

Apple's previous biggest purchase was of NeXT Computer for US$400 million in 1996 - a deal that brought Jobs back to lead the company. But the suggestion that Apple is wallowing in its success irks the team.

"Can't innovate any more, my ass," growled Phil Schiller, Apple's head of marketing as he unveiled a -style version of the Mac Pro desktop computer. But that was a year ago. And the pace of progress in the technology industry is relentless.

In the past week alone Google and Microsoft have shown off a self-driving car and a system that translates between spoken languages in a Skype conversation.

Apple's top executives say they have plenty in store. Cook has promised "some exciting new products … across 2014", while Eddy Cue, who runs Apple's iTunes, Maps and iCloud divisions, said last week: "Later this year, we've got the best product pipeline that I've seen in my 25 years at Apple."

Jan Dawson, of Jackdaw Research, says the iPhone is a historical one-off.

"There's no single product that can ever achieve those levels of revenue growth for Apple again, because nothing shares the ubiquity, subsidy and price characteristics [of the smartphone]. As such, as the iPhone growth slows, if Apple wants to achieve the same sort of growth it's achieved in the past, it's going to need to do it with a large number of products rather than just one," he said.

But what form will new products take? And can Apple still innovate without the ferocious perfectionism of Jobs?

Andrew Graves, professorial fellow of technology management at the University of Bath, said Apple's biggest risk was becoming complacent in the face of success. "I knew Steve Jobs when I was at MIT in the 1980s. He had ideas about electronic books - we all thought he was crazy.

"He was very good at not being complacent."

Cook has always been insistent - as was Jobs - that Apple won't make low-cost products just to chase sales. Instead, his strategy appears to be to tempt people using rival smartphones across to the iPhone, and then capitalise by selling apps that tie people to its platform.

Dawson at Jackdaw Research thinks that will be the way forward. "I don't buy the 'Apple has lost its mojo' stuff. But I do think success can be crippling - when you have a string of hits such as Apple has had."

With iPad sales and the smartphone market slowing, Cook's biggest challenge is to demonstrate he can upset that pattern.

The problem is that - as Steve Ballmer at Microsoft found before him - there's only one place you can go from being the world's largest company.