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#JavaScript (ES6), 26 24 bytes
Saved 2 bytes thanks to @Grimmy
a=>!a.some(n=>2*a>(a=n))
Try it online!
#JavaScript (ES6), 26 26 24 bytes
a=>!a.some(p=n=>2*p>n=>2*a>(p=na=n))
Try it online!Try it online!
#JavaScript (ES6), 26 bytes
a=>!a.some(p=n=>2*p>(p=n))
