Hyers - Ulam Stability Of Two Kinds Of Generalized Additive Set - Valued Functional Equations

In this paper, we first give two kinds of generalized additive set-valued function equations. Then we study the Hyers-Ulam stability of these two kinds of functional equations. The methods we used. are the direct method and the fixed point theorem.According to the content of this article, this paper is divided into the following three chapters.In chapter 1, we recall some basic knowledge of the stability of functional equa-tions.In chapter 2, we first gives the form of two kinds of generalized additive set-valued function equations. Then we use the direct method to prove the Hyers-Ulam stability of these two functional equations. Let X be a real vector space, Y be a Banach space, f:Xâ†' Ccb(Y) be a mapping. If (?)x1,..., xl∈X,f satisfies then f is called the generalized additive set-valued function equation of type 1. If (?)x1,...,xl ∈X,1≤i≤l,f satisfies then f is called the generalized additive set-valued function equation of type 2.In chapter 3, we use the fixed point theorem to prove he Hyers-Ulam stability of these two kinds of functional equations.