The past week saw record-breaking online sales as the U.S. and much of the rest of the Western world gobbled up Thanksgiving weekend sales.

But though an incredible amount of money was spent from Black Friday through Cyber Monday, the results were a mixed bag for ecommerce superstar Amazon (AMZN) .

Many observers say that though Amazon no longer depends on Thanksgiving, Black Friday or Cyber Monday sales as it once did, Chairman, Chief Executive and Founder Jeff Bezos must seriously consider a few challenges to the company's business.

Sales of devices at Amazon over the weekend rose more than 100% from a year earlier. But digging deeper paints a less-than-rosy picture.

This year, Amazon sold two times more Kindle tablets than last year, but on Cyber Monday 2015, the company sold three times more tablets than it had the year before.

Similarly, sales of the Amazon Fire TV streaming-media player also decelerated, up 2.5 times from a year earlier. But Cyber Monday Fire TV sales in 2015 grew more than six times year over year.

Amazon has boasted that it sold millions of its all-new Echo Dot over the holiday weekend.

This lowest-cost version of its Alexa voice-activated personal assistant has made headlines, but the device was marked down to just $40 from nearly $50 in September. It is doubtful whether this momentum can continue at the regular price.

But while Amazon's sales growth is cooling, it is heating up for some of the company's competitors.

For instance, Walmart has redoubled its ecommerce efforts over the past year in an effort to catch up with Amazon, especially when it comes to mobile purchasing. And those initiatives are starting to pay off.

The retail giant reported that its holiday weekend application orders with in-store pickup jumped 150%.

About half of Walmart's orders for pickup were placed on a mobile device or through the retailer's app. More importantly, an estimated 70% of its Cyber Monday traffic came from the mobile segment.

Walmart's stock has shot up nearly 2% while Amazon shares have fallen.

But Walmart isn't the only brick-and-mortar retailer making headway online. Kohl's and Target also beat records for digital sales on Cyber Monday.

Traditional retailers are upping their online ante, and this could pose a bigger threat to Amazon than what analysts or the company itself expect.

Thanksgiving weekend represented a "modestly positive kickoff" to the holiday season, according to analysts at Deutsche Bank.

A large portion of the selling season lies ahead for retailers because fewer people completed their shopping during Thanksgiving weekend and some didn't even start, CNBC reported.

All this doesn't mean that Amazon should be completely counted out. Amazon still sold a very large amount of merchandise over Thanksgiving weekend, but as the holiday season approaches there are other companies that offer more compelling growth stories.

In particular, investors should keep an eye on traditional retailers that are setting their sights on ecommerce.

Three that are improving their online sales and also score high on the American Customer Satisfaction Index are Dillard's, Victoria's Secret parent L Brands and Nordstrom. Macy's and Walmart are also expected to see big online sales growth during the holiday season.

As more consumers turn to online shopping, there are big fortunes to be made by investors, and Amazon is no longer the only game in town.

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The author is an independent contributor who at the time of publication owned none of the stocks mentioned.

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