Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 474
Stability of a generalization of Wilson’s equation on monoid
Karim Farhat, Idriss Ellahiyani, Belaid Bouikhalene
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2393
April 15, 2393

Abstract: Given a character v: G → C \ {0} and an involution σ of a monoid M we study the solutions f, g: M −→ C of the functional equation f(xy) + v(y)f(xσ(y)) = 2f(x)g(y), x, y ∈ M, from the theory of trigonometric functional equations. 1) We show that g satisfies g(xy) +v(y)g(xσ(y)) = 2g(x)g(y) if f not equal to 0. 2) We derive hyperstability results for the equation, when v is unitary.