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Bihom derivations in Banach algebras

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Abstract

In this paper, we introduce bihom derivations in complex Banach algebras. Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of bihom derivations in complex Banach algebras, associated with the bi-additive s-functional inequality \(\Vert f(x+y, z-w) + f(x-y, z+w) -2f(x,z)+2 f(y, w)\Vert \le \Vert s \left( 2f\left( \frac{x+y}{2}, z-w\right) + 2f\left( \frac{x-y}{2}, z+w\right) - 2f(x,z )+ 2 f(y, w)\right) \Vert \), where s is a fixed nonzero complex number with \(|s |< 1\).

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Acknowledgements

This work was supported by Incheon National University Research Grant 2018–2019.

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Authors and Affiliations

  1. Department of Mathematics, Incheon National University, Incheon, 22012, Korea

    Inho Hwang

  2. Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea

    Choonkil Park

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  1. Inho Hwang
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  2. Choonkil Park
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Correspondence to Choonkil Park.

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Hwang, I., Park, C. Bihom derivations in Banach algebras. J. Fixed Point Theory Appl. 21, 81 (2019). https://doi.org/10.1007/s11784-019-0722-y

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  • DOI: https://doi.org/10.1007/s11784-019-0722-y

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