Apple's core beliefs remain the same
I've decided to write this post as I have seen many people saying that Apple has changed their beliefs with products like iPhone 5 ( with the 4 inch display) and iPad mini (7.9 inch display). If you look closely, it's just external factors that made them inevitable to ignore or alter their beliefs.
First, iPhone 5's 4 inch display. - did Apple decide to abandon its belief that 3.5 inch is the perfect size for a smartphone display just because of the popularity of high-end smartphones with giant 4.5+inch displays?
Apple has used 3.5 inch displays for all previous iPhones due to its ease of one-handed operation. The 4 inch display simply doesn't give the user a complete control over all touch elements with one hand on the screen as on the 3.5 inch display. This is a truth despite the advantages of having more viewable screen area and full-screen video playback. So, the 4 inch display has a different set of trade-offs and advantages, and not necessarily a better solution than a 3.5 inch display.
Then why did Apple go with a larger display? It's simply because they needed more space in an iPhone 5 to fit all the hardware they wanted to put in. More specifically, they need more surface area. The addition of LTE chip and other stuff I don't know must have required some extra surface (surface area) that Apple engineers couldn't find any way to fit in a iPhone 4/4S sized design. But they couldn't just increase the height of the phone and let the display stay the same size. It is going to make the phone look weird. So, they turned a problem into a feature.
Second, iPad mini's 7.9 inch display - Tim Cook is against Steve Jobs?
Steve Jobs said that Apple would make never make a 7 inch tablet because the display is just too small to put sufficient touch elements of appropriate size. And you know what? Apple still believes in it because iPad mini has a 7.9 inch display, not 7 inch. You may go: WTH? What's the difference? It turns out, it does makes a lot of difference. The usable screen area of an iPad mini is surprisingly much bigger than that of, say, Nexus 7, especially because it has a 3:2 aspect ratio, making it more ideal for almost all kinds of tasks except for videos. Touch elements are smaller, but still very usable. In other words, iPad mini is in an entirely different class, in terms of product usability and overall experience, from 7 inch tablets. (Of course, consumers won't see it this way.)
Furthermore, if Apple wanted to compete with the 7 inch Android tablets by crushing their initial belief and admitting that 7 inch display is good enough, iPad mini wouldn't have been priced at $329 in the first place. iPad mini isn't a dumbed down iPad; it is another definition of a great tablet that Apple has managed to find out.