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Intuitionistic Fuzzy Approximately Additive Mappings

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Functional Equations in Mathematical Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 52))

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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.

Mathematics Subject Classification (2000): Primary 39B82, 39B52

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Authors and Affiliations

  1. Department of Mathematics, Semnan University, 35195-363, Semnan, Iran

    M. Eshaghi-Gordji, H. Khodaei, H. Baghani & M. Ramezani

Authors
  1. M. Eshaghi-Gordji
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  2. H. Khodaei
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  3. H. Baghani
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  4. M. Ramezani
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Corresponding author

Correspondence to M. Eshaghi-Gordji .

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Editors and Affiliations

  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

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Eshaghi-Gordji, M., Khodaei, H., Baghani, H., Ramezani, M. (2011). Intuitionistic Fuzzy Approximately Additive Mappings. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_9

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