In section 1: When the ‘affine’ word is commonly used, the mixture coeffecient (denoted there by p) can be any real number. When 0≤p≤1, then it’s still an affine combination, but a more precise tern could be ‘convex combination’.
However, as you work with function spaces, convexity in a function space is different then being a convex function, so maybe some new notation should be introduced.
In section 1: When the ‘affine’ word is commonly used, the mixture coeffecient (denoted there by p) can be any real number. When 0≤p≤1, then it’s still an affine combination, but a more precise tern could be ‘convex combination’.
However, as you work with function spaces, convexity in a function space is different then being a convex function, so maybe some new notation should be introduced.