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

Hassan Azadi Kenary () and Themistocles M. Rassias ()
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Hassan Azadi Kenary: College of Sciences, Yasouj University
Themistocles M. Rassias: National Technical University of Athens

A chapter in Applications of Nonlinear Analysis, 2018, pp 507-522 from Springer

Abstract: Abstract In this paper, we prove the Hyers-Ulam-Rassias stability of the following quadratic functional equations f ∑ i = 1 n a i x i + ∑ i = 1 n − 1 ∑ j = i + 1 n f ( a i x i ± a j x j ) = ( 3 n − 2 ) ∑ i = 1 n a i 2 f ( x i ) , $$\displaystyle f\left (\sum _{i=1}^n a_i x_i\right )+\sum _{i=1}^{n-1}\sum _{j=i+1}^nf(a_ix_i\pm a_jx_j)=(3n-2)\sum _{i=1}^n a_{i}^2 f(x_i), $$ where a 1 , ⋯ , a n ∈ ℤ − { 0 } $$a_1,\cdots ,a_n \in \mathbb {Z}-\{0\}$$ 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-89815-5_17

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DOI: 10.1007/978-3-319-89815-5_17

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