In this paper we give complete characterizations, in terms of Dini numbers and integrals, of positive functions $\Phi(u)$ defined in $(0, \infty)$ satisfying the conditions: (i) $\Phi(u)/u^a$ is ...

The Monthly publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional ...

The study of partition functions is a significant area in number theory, focusing on how integers can be expressed as sums of other integers. Recent research has explored various inequalities related ...