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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. Among these was the following question concerning the stability of homomorphisms. We are given a group G and a metric group G′ with metric ρ(·,·). Given > 0, does there exist a δ > 0 such that if f :G→G′ satisfies ρ(… (More)

- Hark-Mahn Kim, Ick-Soon Chang
- Appl. Math. Lett.
- 2012

- Kil-Woung Jun, Hark-Mahn Kim
- 2007

In the present paper, we investigate the situations so that the generalized Hyers-Ulam-Rassias stability for functional equations f(x 2) = f(x)x + xf(x) and f(xy) = f(x)y + xf(y) is satisfied. As a result we obtain that every linear mapping on a commutative Banach algebra which is an ε-approximate derivation maps the algebra into its radical.

In this paper, we investigate homomorphisms from unital C * − algebras to unital Ba-nach algebras and derivations from unital C * − algebras to Banach A− modules related to a Cauchy–Jensen functional inequality.

- Hark-Mahn Kim, Hwan-Yong Shin
- Journal of inequalities and applications
- 2017

The purpose of this paper is to obtain refined stability results and alternative stability results for additive and quadratic functional equations using direct method in modular spaces.

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. Among these was the following question concerning the stability of homomorphisms. Let G1 be a group and let G2 be a metric group with metric ρ ·, · . Given > 0, does there exist a δ > 0 such that if f : G1 → G2… (More)

In this article, we prove the generalized Hyers–Ulam stability of the following Cauchy additive functional equation f x − y n + z + f y − z n + x + f z − x n + y = f (x + y + z) in fuzzy Banach spaces for any fixed nonzero integer n. A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull.

- Madjid Eshaghi Gordji, Hamid Khodaei, Hark-Mahn Kim
- Int. J. Math. Mathematical Sciences
- 2011

we establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability in p-Banach spaces.