A refinement of Egghe's increment studies: an alternative version

In this contribution we show how results obtained in a series of papers by Egghe can be refined in the sense that we need fewer conditions. In these articles Egghe considered a general h-type index which has a value n if n is the largest natural number such that the first n publications (ranked according to the number of received citations) have received at least f(n) citations, with f(n) any increasing function defined on the strictly positive numbers. His results deal with increments I2 and I1 defined by: I2(n)= I1(n+1)-I1n) where I1(n)=(n+1)f(n+1)-nf(n). Our results differ from Egghe’s because we also consider I0(n) = nf(n). This version differs from the original one (Rousseau, 2014) by the fact that we (try to) use standard methods for solving difference equations. These methods are recalled in an appendix