An Alternative Equation for Generalized Polynomials of Degree Two

Zoltán Boros; Rayene Menzer

doi:10.2478/amsil-2023-0017

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An Alternative Equation for Generalized Polynomials of Degree Two

Annales Mathematicae Silesianae

Volume 38 (2024): Issue 2 (September 2024)

By: Zoltán Boros and Rayene Menzer

Open Access

|Oct 2023

Abstract

In this paper we consider a generalized polynomial f: ℝ → ℝ of degree two that satisfies the additional equation f(x)f(y) = 0 for the pairs (x, y) ∈ D, where D ⊆ ℝ² is given by some algebraic condition. In the particular cases when there exists a positive rational m fulfilling $D = {(x, y) \in ℝ^{2} | x^{2} - m y^{2} = 1},$ D = \left\{ {\left( {x,y} \right) \in \mathbb{R}{^2}|{x^2} - m{y^2} = 1} \right\}, we prove that f(x) = 0 for all x ∈ ℝ.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2023-0017 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 214 - 220

Submitted on: Apr 25, 2023

Accepted on: Oct 3, 2023

Published on: Oct 26, 2023

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

additive functions,

quadratic functions,

generalized polynomials,

alternative equation

Related subjects:

Mathematics,

General mathematics

© 2023 Zoltán Boros, Rayene Menzer, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 38 (2024): Issue 2 (September 2024)