inside any component without having to first import them and then prepend this to the function name

What you described is mixin.

Vue.mixin({
  methods: {
    capitalizeFirstLetter: str => str.charAt(0).toUpperCase() + str.slice(1)
  }
})

This is a global mixin. with this ALL your components will have a capitalizeFirstLetter method, so you can call this.capitalizeFirstLetter(...) from component methods or you can call it directly as capitalizeFirstLetter(...) in component template.

Working example: http://codepen.io/CodinCat/pen/LWRVGQ?editors=1010

See the documentation here: https://vuejs.org/v2/guide/mixins.html