Journal: | Proyecciones (Antofagasta) |
Database: | PERIÓDICA |
System number: | 000405879 |
ISSN: | 0716-0917 |
Authors: | Sahoo, Prasanna K1 |
Institutions: | 1University of Louisville, Department of Mathematics, Louisville, Kentucky. Estados Unidos de América |
Year: | 2017 |
Season: | Mar |
Volumen: | 36 |
Number: | 1 |
Pages: | 13-27 |
Country: | Chile |
Language: | Inglés |
Document type: | Artículo |
Approach: | Analítico |
English abstract | Let G be a group and C the field of complex numbers. Suppose σ1, σ2 : G → G are endomorphisms satisfying the condition σi(σi(x)) = x for all x in G and for i = 1, 2. In this paper, we find the central solution f : G → C of the equation f(xy) + f(σ1(y)x) = 2f(x) + f(y) + f(σ2(y)) for all x, y ∈ G which is a variant of the Drygas functional equation with two involutions. Further, we present a generalization the above functional equation and determine its central solutions. As an application, using the solutions of the generalized equation, we determine the solutions f, g, h, k : G×G → C of the functional equation f(pr, qs) + g(sp, rq)=2f(p, q) + h(r, s) + k(s, r) when f satisfies the condition f(pr, qs) = f(rp, sq) for all p, q, r, s ∈ G |
Disciplines: | Matemáticas |
Keyword: | Matemáticas puras, Ecuaciones funcionales, Desigualdades, Teoría de grupos |
Keyword: | Mathematics, Pure mathematics, Functional equations, Inequalities, Group theory |
Full text: | Texto completo (Ver PDF) |