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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) = 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 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 paper, we investigate homomorphisms from unital C∗−algebras to unital Banach algebras and derivations from unital C∗−algebras to Banach A−modules related to a Cauchy–Jensen functional inequality. Mathematics subject classification (2010): 39B72, 46H30, 46B06.

In this article, we prove the generalized Hyers–Ulam stability of the following Cauchy additive functional equation

- 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.