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In 1940, Ulam  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)
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
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.