Year: 2025
Type: article
Abstract: In this paper, we present an alternative proof of Fekete’s Lemma. We demonstrate that for any subadditive sequence, it is possible to construct a subadditive function that exactly interpolates the sequence. Using this result, along with Hille’s theorem on subadditive functions, we naturally arrive at Fekete’s Lemma. Additionally, we provide an explicit formula for determining the largest subadditive minorant of a given sequence. We explore a sandwich-type result and derive a discrete version of the Hyers-Ulam type stability theorem. For approximately periodic sequences, we offer a decomposition result. In the final section, we propose two characterization theorems for ordinary periodic sequences. The motivation, research progress, and other important details are covered in the introduction.
Source: Results in Mathematics
Author: Angshuman R. Goswami
Institution: University of Pannonia
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Pannon Egyetem
OpenAlex ID: W4411195664