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Additive s-functional inequality and hom-derivations in Banach algebras

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Abstract

In this paper, we introduce and solve the following additive s-functional inequality:

$$\begin{aligned} \left\| f\left( x+y\right) - f(x )- f(y)\right\| \le \Vert s (f(x-y)-f(x)-f(-y))\Vert , \end{aligned}$$
(0.1)

where s is a fixed nonzero complex number with \(|s|<1\). Using the fixed point method and the direct method, we prove the Hyers–Ulam stability of the additive s-functional inequality (0.1) in complex Banach spaces. Furthermore, we prove the Hyers–Ulam stability of hom-derivations in complex Banach algebras.

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Acknowledgements

This research was supported by the Daejin University Research Grant.

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Correspondence to Jung Rye Lee.

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Park, C., Lee, J.R. & Zhang, X. Additive s-functional inequality and hom-derivations in Banach algebras. J. Fixed Point Theory Appl. 21, 18 (2019). https://doi.org/10.1007/s11784-018-0652-0

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  • DOI: https://doi.org/10.1007/s11784-018-0652-0

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