Functional Inequalities Associated with Jordan-von Neumann-Type Additive Functional Equations.

The article presents a research regarding the association between Jordan-von Neumann-type additive functional equations and functional inequalities. It proves the generalized Hyers-Ulam stability of the following functional inequalities: ρf(x)+f(y)+f(z)ρ ≤ ρ 2f((x+y+z)/2)ρ, ρf(x)+f(y)+f(z) ρ ≤ ρf(x+y+z)ρ, ρ f(x)+f(y)+2f(z)ρ ρ2f((x+y)/2+z)ρ in the spirit of the Rassias stability method for approximately homomorphisms. According to the report, the inequality that was brought in for the first time by Rassias provided a lot of influence in the development of a generalization relating to the Hyers-Ulam stability concept.