Intuitionistic Fuzzy Approximately Additive Mappings

M. Eshaghi-Gordji (), H. Khodaei (), H. Baghani () and M. Ramezani ()
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M. Eshaghi-Gordji: Semnan University
H. Khodaei: Semnan University
H. Baghani: Semnan University
M. Ramezani: Semnan University

Chapter Chapter 9 in Functional Equations in Mathematical Analysis, 2011, pp 107-124 from Springer

Abstract: Abstract In this paper, we investigate the generalized Hyers–Ulam stability and the intuitionistic fuzzy continuity of the generalized additive functional equation $$\begin{array}{rcl} & & {2}^{n-1}\;{a}_{ 1}f({x}_{1}) = f\bigg{(}\sum\limits_{i=1}^{n}{a}_{ i}{x}_{i}\bigg{)} \\ & & \quad +\sum\limits_{k=2}^{n}\ \sum\limits_{{i}_{1}=2}^{k}\ \sum\limits_{{i}_{2}={i}_{1}+1}^{k+1}\ldots \sum\limits_{{i}_{n-k+1}={i}_{n-k}+1}^{n}f\left (\sum\limits_{{ i=1 \atop i\neq {i}_{1},\ldots,{i}_{n-k+1}} }^{n}{a}_{ i}{x}_{i} -\sum\limits_{r=1}^{n-k+1}{a}_{{ i}_{r}}{x}_{{i}_{r}}\right )\\ \end{array}$$ in intuitionistic fuzzy Banach spaces, where $$n \in \mathbb{N}\setminus \{1\}$$ and $${a}_{1},\ldots,{a}_{n} \in \mathbb{Z}\setminus \{0\}$$ with a 1≠ ± 1.

Keywords: Intuitionistic fuzzy normed space; Additive functional equation; Intuitionistic fuzzy stability; Intuitionistic fuzzy continuity (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4614-0055-4_9

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