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Stability of an n-Dimensional Functional Equation in Banach Space and Fuzzy Normed Space

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Abstract

In this paper, the authors investigate the general solution of a new additive functional equation

$$\displaystyle f\left (\sum ^{n}_{i=1}x_i\right )+\sum _{{j=1; i \neq j}}^{n}f\left (-x_j-x_i+\sum _{1\leq i < j < k \leq n}x_{k}\right ){=}\left (\frac {n^2-5n+6}{2}\right ) \sum ^{n}_{i=1}f\left (x_i\right )\\ $$

where n is a positive integer with \(\mathbb {N}-\{1,2,3,4 \}\) and discuss its generalized Hyers–Ulam stability in Banach spaces and stability in fuzzy normed spaces using two different methods.

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Author information

Authors and Affiliations

  1. Departmento de Ciências Exatas e Engenharia, Academia Militar, Lisboa, Portugal

    Sandra Pinelas

  2. Department of Mathematics, Sri Vidya Mandir Arts and Science College, Uthangarai, Tamil Nadu, India

    V. Govindan

  3. Department of Mathematics, Government Arts and Science College (for Men), Krishnagiri, Tamil Nadu, India

    K. Tamilvanan

Authors
  1. Sandra Pinelas
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  2. V. Govindan
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  3. K. Tamilvanan
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  2. Pedagogical Department E. E., Section of Mathematics and Informatics, National and Kapodistrian University of Athens, Athens, Greece

    John Michael Rassias

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Pinelas, S., Govindan, V., Tamilvanan, K. (2019). Stability of an n-Dimensional Functional Equation in Banach Space and Fuzzy Normed Space. In: Anastassiou, G., Rassias, J. (eds) Frontiers in Functional Equations and Analytic Inequalities. Springer, Cham. https://doi.org/10.1007/978-3-030-28950-8_10

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