Stability of an alternative functional equation related to Jensen's functional equation

Abstract

ABSTRACT:Given an integer λ = 1, we verify the Hyers-Ulam stability of the alternative Jensen's functional equationswhere f is a mapping from a 2-divisible group to a Banach space and λ is an integer.

Ulam Stability of Jensen Functional Inequality on a Class of Noncommutative Groups

“…In this section, we will prove the Hyers-Ulam stability of the Jensen's functional inequality (3) when jρj < 1 is an integer by the so-called direct method. The stability results of Jensens functional equation can be found in, for instance, Srisawat [30]. Suppose that G is a group and E is a real Banach space.…”