Stability of   -­variable Additive and   -­variable Quadratic Functional Equations

Govindan, Vediyappan; Govindan, Vediyappan; Pinelas, Sandra; Pinelas, Sandra; Lee, Jung Rye; Lee, Jung Rye

doi:https://doi.org/10.7468/jksmeb.2022.29.2.179

P-ISSN3059-0604
E-ISSN3059-1309
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Vol.29 No.2

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Stability of -variable Additive and -variable Quadratic Functional Equations

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

2022, v.29 no.2, pp.179-188

https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.2.179

Govindan, Vediyappan
Pinelas, Sandra
Lee, Jung Rye

Govindan,, V. , Pinelas,, S. , & Lee,, J. R. (2022). Stability of -variable Additive and -variable Quadratic Functional Equations. , 29(2), 179-188, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.2.179

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Abstract

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form <TEX>

f \(\sum_{i = 1}^{s} x_{i} \) + \sum_{j = 1}^{s} f \(- s x_{j} + \sum_{i = 1, i \neq j}^{s} x_{i} \) = 0

$f$\sum\limits_{i=1}^{s}x_i$+\sum\limits_{j=1}^{s}f$-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i$=0$ </TEX> and <TEX>

f \(\sum_{i = 1}^{l} x_{i} \) + \sum_{j = 1}^{l} f \(- l x_{j} + \sum_{i = 1, i \neq j}^{l} x_{i} \) = (l + 1)

$f$\sum\limits_{i=1}^{l}x_i$+\sum\limits_{j=1}^{l}f$-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i$=(l+1)$ </TEX><TEX>$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$</TEX> (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

keywords: Hyers-Ulam stability, additive and quadratic mapping, quasi-Banach space, p-Banach space

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Article Contents

Vol.29 No.2

Stability of -­variable Additive and -­variable Quadratic Functional Equations

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics

Stability of -variable Additive and -variable Quadratic Functional Equations