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Apple is estimated to have sold 55.3 million iPhones in Q1 2014, helped by sales of the new iPhone 5s, pictured above.

Analysts are estimating that Apple sold more than 55 million iPhones in the last three months of 2013, which would be the most smartphones the company has ever sold in a single quarter.

Tim Cook, fresh from his trip to Beijing for the launch of the iPhone on China Mobile (the world's biggest mobile operator in terms of subscribers), will be announcing the sales figures for the three months to the end of December 2013 during a conference call with analysts next Monday.

It will be the first full quarter when Apple has sold two new iPhones at once, following the launch of the iPhone 5s and the iPhone 5c in September.

Apple's new flagship iPhone 5s and its cheaper, colourful cousin the iPhone 5c went on sale on 20 September, complete with a completely redesigned operating system iOS 7, together with updates to its iPad, iMac and MacBook Pro ranges.

50 - 59 million iPhones

The results for the last reported quarter (July-September), included 10 days of sales of the new Apple smartphones and saw iPhone sales growing by 26% compared to the same period in 2012 (26.9 million vs 33.8 million).

According to the average estimate from 44 analysts compiled by Fortune's Philip Elmer-Dewitt, the tech giant is expected to top its previous sales record, selling 55.3 million iPhones, up 16% from the same quarter last year.

The highest estimate, from Faizal Kara of the Braeburn Group was 59.73 million, whilst the lowest estimate, 50 million, came from Ilari Scheinin, also of the Braeburn Group.

Christmas

The big reasons for the record sales are the launch of the new smartphones, the Christmas season, as well as the introduction of the optional within-contract phone upgrades now offered by mobile operators.

These new contract types - such as O2 Refresh, Vodafone Red and EE's Early Upgrade - allow you to uprade to a new smartphone at any time, as long as you are willing to pay a cost towards the phone, if it is a high-end smartphone.

Data released on Friday from research firm NDP found that Apple, which had been struggling against its Android rivals, has succeeded in beating Samsung to gain 42% of the smartphone market in the US in the last quarter.

Apple reported its first profit decline in a decade in April 2013, when profits dropped to $9.5 billion (£5.78bn, €7bn) from $11.6bn in the same period of 2012, despite posting record revenues of $43.6bn.

Samsung and the Android OS began to dominate global smartphone market share in 2012, even though Apple has continued to make more money on the handsets it sells.

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