Relations between I-approximate Dini derivatives and monotonicity are presented. Next, some generalizations of the Denjoy–Young–Saks Theorem
for I-approximate Dini derivatives of an arbitrary real function are proved.
The Hirsch index is a number that synthesizes a researcher’s output. It is defined as the maximum number h such that the researcher has h papers with at least h citations each. Woeginger (Math Soc Sci 56: 224–232, 2008a; J Informetr 2: 298–303, 2008b) suggests two axiomatic characterizations
of the Hirsch index using monotonicity as one of the axioms. This note suggests three characterizations without adopting the
Cecchi , M. , Marini , M. , Villari , G. 1989 On the monotonicity property for a certain class of second order differential equations J. Differential Equations 82 15 – 27 10.1016/0022-0396(89)90165-4 .