On a Functional Equation Arising From Proth Identity

Chung, Jaeyoung; Sahoo, Prasanna K.

doi:10.4134/ckms.2016.31.1.131

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2022

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Cited by 3 publications

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“…Inspired by papers [6,8,7], we will describe the solutions f : R 2 → S of the functional equation (E(α, β)). Let H be the set defined by…”

Section: Resultsmentioning

confidence: 99%

A Parametric Functional Equation Originating from Number Theory

Mouzoun

Zeglami

Aissi

2022

Annales Mathematicae Silesianae

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Let S be a semigroup and α, β ∈ ℝ. The purpose of this paper is to determine the general solution f : ℝ2 → S of the following parametric functional equation f ( x 1 + x 2 + α y 1 y 2 , x 1 y 2 + x 2 y 1 + β y 1 y 2 ) = f ( x 1 , y 1 ) f ( x 2 , y 2 ) , f\left( {{x_1} + {x_2} + \alpha {y_1}{y_2},{x_1}{y_2} + {x_2}{y_1} + \beta {y_1}{y_2}} \right) = f\left( {{x_1},{y_1}} \right)f\left( {{x_2},{y_2}} \right), for all (x 1, y 1), (x 2, y 2) ∈ ℝ2, that generalizes some functional equations arising from number theory and is connected with the characterizations of the determinant of matrices.

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“…Inspired by papers [6,8,7], we will describe the solutions f : R 2 → S of the functional equation (E(α, β)). Let H be the set defined by…”

Section: Resultsmentioning

confidence: 99%

A Parametric Functional Equation Originating from Number Theory

Mouzoun

Zeglami

Aissi

2022

Annales Mathematicae Silesianae

View full text Add to dashboard Cite

show abstract

“…3) or there are other solutions. This question was addressed by Chávez and Sahoo [4] (and subsequently fixed an error in [4] by Chung and Sahoo [5]) in the following theorem. One of the well known properties of matrices is the following: The determinant of the product of two square matrices is the product of their determinants.…”

Section: Introductionmentioning

confidence: 94%