On Log-Concave Operator Acting on Sequences and Series

Abstract

In this paper, we investigate the properties of sequences and series under the action of the log-concave operator \(\mathcal{L}\). We explore the relationship between the convergence of a sequence \((a_k)\) and the convergence of sequences and series derived by applying \(\mathcal{L}\) iteratively. These results demonstrate the strong regularity properties of log-concave sequences and provide a framework for analyzing the convergence of sequences and series derived from the log-concave operator. The findings have implications for combinatorics, probability, optimization, and related fields, opening new avenues for further research on the behavior of log-concave sequences and their associated operators.