Some functional equations in the spaces of generalized functions

Abstract

Making use of the fundamental solution of the heat equation we find the solutions of some functional equations such as the Cauchy equations, Pexider equations, quadratic functional equations and d'Alembert equations in the spaces of Schwartz distributions and Sato hyperfunctions. Mathematics Subject Classification (2000). 39B22, 46F05.

On the stability of a mixed type functional equation in generalized functions

“…Making use of similar approaches in [15][16][17][18][19][20], we reformulate equation (1.1) and the related inequality for the spaces of generalized functions as follows:…”

Stability of an additive functional equation in the spaces of generalized functions

“…In this article, in a similar manner as in [15][16][17][18][19], we solve the general solutions and the stability problems of (1.2) in the spaces of generalized functions such as the space S (Ê m ) of tempered distributions, the space F (Ê m ) of Fourier hyperfunctions and the space D (Ê m ) of distributions. Using the notions as in [15][16][17][18][19], we first reformulate (1.2) and the related inequality in the spaces of generalized functions as follows: 4) where A, P i and B ij are the functions defined by…”

“…Using the notions as in [15][16][17][18][19], we first reformulate (1.2) and the related inequality in the spaces of generalized functions as follows: 4) where A, P i and B ij are the functions defined by…”

Distributional method for the D′ Alembert equation

“…∂ α n n , where N 0 is the set of non-negative integers and ∂ j = ∂/∂x j . We refer to [1], [5], [6], [7], [11] for more details about the space D (R n ) of distributions.…”