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A Fixed Point Approach to Stability of the Quadratic Equation

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Topics in Mathematical Analysis and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 94))

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Abstract

In this paper, by using the fixed point method in Banach spaces, we prove the Hyers–Ulam–Rassias stability for the quadratic functional equation

$$\displaystyle{f\left (\sum _{i=1}^{m}x_{ i}\right ) =\sum _{ i=1}^{m}f(x_{ i}) + \frac{1} {2}\sum _{1\leq i<j\leq m}\{f(x_{i} + x_{j}) - f(x_{i} - x_{j})\}.}$$

The concept of the Hyers–Ulam–Rassias stability originated from Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72(2), 297–300 (1978).

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Author information

Authors and Affiliations

  1. Laboratory LAMA, Harmonic Analysis and Functional Equations Team, Department of Mathematics, Faculty of Sciences, University of Ibn Tofail, Kenitra, Morocco

    M. Almahalebi, A. Charifi & S. Kabbaj

  2. Department of Mathematics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco

    E. Elqorachi

Authors
  1. M. Almahalebi
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  2. A. Charifi
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  3. S. Kabbaj
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  4. E. Elqorachi
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Correspondence to E. Elqorachi .

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Editors and Affiliations

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

    Themistocles M. Rassias

  2. Department of Mathematics, University of Pécs, Pécs, Hungary

    László Tóth

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Almahalebi, M., Charifi, A., Kabbaj, S., Elqorachi, E. (2014). A Fixed Point Approach to Stability of the Quadratic Equation. In: Rassias, T., Tóth, L. (eds) Topics in Mathematical Analysis and Applications. Springer Optimization and Its Applications, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-06554-0_3

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