Asymptotic Behaviors of Set-Valued Cauchy and Jensen Functional Equations

Let  X be a normed vector space and Y  a Banach space. In this paper, we establish the conditional stability of the set-valued  functionalequations\begin{align*}   & f(x+y)+K=f(x)+f(y), \\  &  ۲f\left(\frac{x+y}{۲}\right)= f(x)+f(y),\\   & ۳f\left(\frac{x+y+z}{۳}\right)= f(x)+f(y)+f(z),\\   & f(x+y)=g(x)+h(y),\end{align*}on various restricted domains, where f,g,h are unknown mappings  from X to cc(Y) and K\in cc(Y), where cc(Y) is the collection of all nonempty, compact, and convex subsets of Y. In addition, we study the asymptotic behaviors of these functional equations.

کلیدواژه ها:

Set-valued mapping ، stability ، Jensen's functional equation ، Asymptotic behavior