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On the Generalized Hyers–Ulam Stability in Multi-Banach Spaces Associated to a Jensen-type Additive Mapping

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Abstract

Using the fixed point method, we prove the generalized Hyers–Ulam–Rassias stability of the following functional equation in multi-Banach spaces:

$$\begin{aligned} f\left(\frac{\sum_{i=1}^{n}r_ix_i}{k}\right)+ \sum_{1 \le i < j \le n}f\left(\frac{r_ix_i +r_jx_j}{k}\right) = \frac{n}{k}\sum_{i=1}^{n}r_if(x_i).\end{aligned}$$
((1))

The concept of generalized Hyers–Ulam–Rassias stability originated from Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72, 297–300, 1978.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Sahand University of Technology, Tabriz, Iran

    Fridoun Moradlou

  2. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Themistocles M. Rassias

Authors
  1. Fridoun Moradlou
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  2. Themistocles M. Rassias
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Correspondence to Fridoun Moradlou .

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Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Dept. Industrial & Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Moradlou, F., Rassias, T. (2014). On the Generalized Hyers–Ulam Stability in Multi-Banach Spaces Associated to a Jensen-type Additive Mapping. In: Rassias, T., Pardalos, P. (eds) Mathematics Without Boundaries. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1106-6_14

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