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Stability of functional equations of n-Apollonius type in fuzzy ternary Banach algebras

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Abstract

Using the fixed point method, we investigate the generalized Hyers–Ulam stability of the ternary homomorphisms and ternary derivations between fuzzy ternary Banach algebras for the additive functional equation of n-Apollonius type, namely

$${\sum_{i=1}^{n} f(z-x_{i}) = -\frac{1}{n} \sum_{1 \leq i < j \leq n} f(x_{i}+x_{j}) + n f (z-\frac{1}{n^{2}} \sum_{i=1}^{n}x_{i}),}$$

where \({n \geq 2}\) is a fixed positive integer.

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Authors and Affiliations

  1. School of Science, Hubei University of Technology, Wuhan, Hubei, 430068, China

    Zhihua Wang

  2. Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA

    Prasanna K. Sahoo

Authors
  1. Zhihua Wang
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  2. Prasanna K. Sahoo
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Correspondence to Zhihua Wang.

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Wang, Z., Sahoo, P.K. Stability of functional equations of n-Apollonius type in fuzzy ternary Banach algebras. J. Fixed Point Theory Appl. 18, 721–735 (2016). https://doi.org/10.1007/s11784-016-0292-1

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