On the approximate solution of D'Alembert type equation originating from number theory

We solve the functional equation E(α) : f(x₁x₂+ αy₁y₂, x₁y₂ + x₂y₁) + f(x₁x₂ ̶ αy₁y₂, x₂y₁ ̶ x₁y₂) = 2f(x₁, y₁)f(x₂, y₂), where (x₁, y₁), (x₂, y₂) ∈ ℝ², f : ℝ² → ℂ and α is a real parameter, on the monoid ℝ². Also we investigate the stability of this equation in the following setting: ⃒f(x₁x₂ + αy₁y₂, xy₂ + x₂y₁) + f(x₁x₂ ̶ αy₁y₂, x₂y₁ ̶ x₁y₂) ̶ 2f(x₁, y₁) f (x₂, y₂)⃒ ≤ min{φ(x₁), ψ(y₁), ϕ(x₂), ζ(y₂)}. From this result, we obtain the superstability of this equation.peerReviewe

On the approximate solution of D'Alembert type equation originating from number theory

We solve the functional equation E(α) : f(x₁x₂+ αy₁y₂, x₁y₂ + x₂y₁) + f(x₁x₂ ̶ αy₁y₂, x₂y₁ ̶ x₁y₂) = 2f(x₁, y₁)f(x₂, y₂), where (x₁, y₁), (x₂, y₂) ∈ ℝ², f : ℝ² → ℂ and α is a real parameter, on the monoid ℝ². Also we investigate the stability of this equation in the following setting: ⃒f(x₁x₂ + αy₁y₂, xy₂ + x₂y₁) + f(x₁x₂ ̶ αy₁y₂, x₂y₁ ̶ x₁y₂) ̶ 2f(x₁, y₁) f (x₂, y₂)⃒ ≤ min{φ(x₁), ψ(y₁), ϕ(x₂), ζ(y₂)}. From this result, we obtain the superstability of this equation.peerReviewe

Superstability of approximate cosine type functions on the monoid ℝ²

In this paper, we study the superstability problem for the cosine type functional equation f(x₁x₂, x₁y₂ + x₂y₁) + f(x₁x₂, y₁x₂ ‒ x₁y₂) = 2 f(x₁, y₁) f(x₂, y₂) on the commutative monoid (ℝ²,X). As a result we obtain cosine type functions satisfying the equation approximately.peerReviewe

Recognition of Tifinagh Characters using Self Organizing Map and Fuzzy k-Nearest Neighbor

In this paper we present a comparison between SOM (Self-Organization Map) neural network and Fuzzy Knearest Neighbor algorithms and their application to handwriting Tifinagh character recognition.The Box approach proposed in [1] is used for features extraction. Experimentation is carried out on a limited database of nearly 200 samples. The results showed that Fuzzy K-Nearest Neighbor had a very good performance

Operatorial approach to the non-Archimedean stability of a Pexider K-quadratic functional equation

AbstractWe use the operatorial approach to obtain, in non-Archimedean spaces, the Hyers–Ulam stability of the Pexider K-quadratic functional equation∑k∈Kf(x+k·y)=κg(x)+κh(y),x,y∈E,where f,g,h:E→F are applications and K is a finite subgroup of the group of automorphisms of E and κ is its order

Utilisation des Réseaux de Neurones pour la Reconnaissance des Caractères Tifinaghe Manuscrits

Cet article présente un système de reconnaissances de caractères tifinaghe manuscrits (SRCTM). Ce système est morcelé en plusieurs composants. L’un de ces composants est le réseau de neurones (le perceptron multicouches PMC) qui se charge de la classification. Un autre composant basé sur la morphologie mathématique permet d’extraire les attributs caractéristiques. Le composant restant se charge des fonctions de prétraitement comme l’acquisition, la numérisation et la normalisation. Notre approche est testée sur une base de données de caractères tifinaghe manuscrits isolés de tailles conséquentes (900 images en apprentissage et 2340 exemples en test). Le taux de reconnaissance trouvé est de 84,91%. Le classificateur utilisé (PMC) montre des résultats suffisamment bons

Système de reconnaissance automatique de la parole Amazigh à base de la transcription en alphabet Tifinagh

Dans ce travail, nous présentons un système de reconnaissance automatique de la parole Amazigh basé sur la transcription en alphabet Tifinagh reconnue par l’Institut Royal de la Culture Amazigh (IRCAM ). Nous avons utilisé le modèle de Markov caché et on a fait une comparaison avec la méthode de programmation dynamique