The main purpose of this paper is to prove the Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen's functional equation for a large class of restricted domains. 1. Introduction. The starting point of studying the stability of functional equations seems to be the famous talk of Ulam ...

The goal of this paper is to investigate the Generalized Hyers - Ulam Rassias (HUR) stability generalquartic functional equation (GQFE) fq(kr1 + (k -1)r2) = 2k4fq(r1) 2(k -1)4fq(r2) +6k2(k -1)2[fq(r1 r2) fq(r1 r2)] 12k2(k 1)2[fq(r1) fq(r2)] in fuzzy normed spaces (F.N. spaces). proved by using direct method. sense and Ulam- Gavruta also studied.

In 1940, Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems, containing the stability problem of homomorphisms as follows Let G1 be a group and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for a...

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we introduce generalized additive mappings of Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative additive mappings.

Suppose A is a Banach algebra without order. We show that an approximate multiplier T : A → A is an exact multiplier. We also consider an approximate multiplier T on a Banach algebra which need not be without order. If, in addition, T is approximately additive, then we prove the Hyers-Ulam-Rassias stability of T. 1. Introduction and statement of results. It seems that the stability problem of f...