an:06252759
Zbl 1282.39030
Jang, Sun; Park, Choonkil; Cho, Young
Hyers-Ulam stability of a generalized additive set-valued functional equation
EN
J. Inequal. Appl. 2013, Paper No. 101, 6 p. (2013).
00328491
2013
j
39B82 39B55
Hyers-Ulam stability; generalized additive set-valued functional equation; closed set; convex set; cone
Summary: We define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation:
\[
f(x_1+\dots+x_l)=(l-1)f\left(\frac{x_1 + \dots+x_{l-1}}{l-1}\right)+f(x_l)
\]
for a fixed integer \(l\) with \(l > 1\), and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.