Mathematical theory of the h‐ and g‐index in case of fractional counting of authorship

This article studies the h‐index (Hirsch index) and the g‐index of authors, in case one counts authorship of the cited articles in a fractional way. There are two ways to do this: One counts the citations to these papers in a fractional way or one counts the ranks of the papers in a fractional way as credit for an author. In both cases, we define the fractional h‐ and g‐indexes, and we present inequalities (both upper and lower bounds) between these fractional h‐ and g‐indexes and their corresponding unweighted values (also involving, of course, the coauthorship distribution). Wherever applicable, examples and counterexamples are provided. In a concrete example (the publication citation list of the present author), we make explicit calculations of these fractional h‐ and g‐indexes and show that they are not very different from the unweighted ones.