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Applications of Nonlinear Analysis pp 507–522Cite as

On the HUR-Stability of Quadratic Functional Equations in Fuzzy Banach Spaces

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 134))

Abstract

In this paper, we prove the Hyers-Ulam-Rassias stability of the following quadratic functional equations

$$\displaystyle f\left (\sum _{i=1}^n a_i x_i\right )+\sum _{i=1}^{n-1}\sum _{j=i+1}^nf(a_ix_i\pm a_jx_j)=(3n-2)\sum _{i=1}^n a_{i}^2 f(x_i), $$

where \(a_1,\cdots ,a_n \in \mathbb {Z}-\{0\}\) and l ∈{1, 2, ⋯ , n − 1}, a l ≠ 1 and a n = 1, where n is a positive integer greater or at least equal to two, in fuzzy Banach spaces.

The concept of 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. Am. Math. Soc. 72 (1978), 297–300.

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Author information

Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yasouj University, Yasouj, Iran

    Hassan Azadi Kenary

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

    Themistocles M. Rassias

Authors
  1. Hassan Azadi Kenary
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  2. Themistocles M. Rassias
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Correspondence to Hassan Azadi Kenary .

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Editors and Affiliations

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

    Themistocles M. Rassias

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Kenary, H.A., Rassias, T.M. (2018). On the HUR-Stability of Quadratic Functional Equations in Fuzzy Banach Spaces. In: Rassias, T. (eds) Applications of Nonlinear Analysis . Springer Optimization and Its Applications, vol 134. Springer, Cham. https://doi.org/10.1007/978-3-319-89815-5_17

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