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{align*} & f(x+y)+K=f(x)+f(y), \\ & 2f(x+y/2)= f(x)+f(y),\\ & 3f(x+y+z/3)= f(x)+f(y)+f(z),\\ & f(x+y)=g(x)+h(y),{align*}on various restricted domains, where $f,g,h$ are unknown mappings from X to $cc(Y)$ and K∈ 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.