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Hyers–Ulam Stability of General Jensen-Type Mappings in Banach Algebras

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Abstract

Using the fixed point method, we prove the Hyers–Ulam stability of homomorphisms in complex Banach algebras and complex Banach Lie algebras and also of derivations on complex Banach algebras and complex Banach Lie algebras for the general Jensen-type functional equation f(α x + β y) + f(α x − β y) = 2α f(x) for any \({\alpha, \beta \in \mathbb{R}}\) with \({\alpha, \beta \neq 0}\). Furthermore, we prove the hyperstability of homomorphisms in complex Banach algebras for the above functional equation with α = β = 1.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, ShenYang University of Technology, Shenyang, 110178, People’s Republic of China

    Gang Lu

  2. Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, 133-791, South Korea

    Choonkil Park

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  1. Gang Lu
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  2. Choonkil Park
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Correspondence to Gang Lu.

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Lu, G., Park, C. Hyers–Ulam Stability of General Jensen-Type Mappings in Banach Algebras. Results. Math. 66, 385–404 (2014). https://doi.org/10.1007/s00025-014-0383-5

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