Infinite sequences and their h-type indices

Starting from the notion of h-type indices for infinite sequences we investigate if these indices satisfy natural inequalities related to the arithmetic, the geometric and the harmonic mean. If f denotes an h-type index, such as the h- or the g-index, then we investigate inequalities such as min(f(X),f(Y)) ≤ f((X + Y)/2) ≤ max(f(X), f(Y)). We further investigate if: f(min(X,Y)) = min(f(X),f(Y)) and if f(max(X,Y)) = max(f(X),f(Y)). It is shown...