A note on monomials

2012/03/14 by J. M. Almira, Almira, J. M., Kh. F. Abu-Helaiel +1
Mathematics · #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical and Theoretical Analysis #math.CA

paper · pdf · doi:10.48550/arxiv.1203.3222

12 pages, submitted to a Journal

arxiv created 2012/03/14 · openalex publication_date 2012/03/14 · arxiv updated 2012/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study discontinuous solutions of the monomial equation (1)/(n!)Δ_hⁿf(x)=f(h). In particular, we characterize the closure of their graph, G(f)^ℝ2, and we use the properties of these functions to present a new proof of the Darboux type theorem for polynomials and of Hamel's theorem for additive functions.

Related

• On the diophantine equation An!+Bm!=f(x,y)
• Schur-like numbers and a lemma of Shearer
• Diophantus Equations and Partially Ordered Sets
• A functional equation for monomial functions
• Diophantine equations involving double factorials