Stability of a quadratic Jensen type functional equation in the spaces of generalized functions

[摘要] Making use of the fundamental solution of the heat equation we find the solution and prove the stability theorem of the quadratic Jensen type functional equation 9f((3)/(x + y + z)) + f(x) + f(y) + f(z) = 4[f((2)/(x + y)) + f((2)/(y + z)) + f((2)/(z + x))] in the spaces of Schwartz tempered distributions and Fourier hyperfunctions. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] quadratic functional equation;Jensen functional equation;stability;generalized function;heat kernel;Gauss transform