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ISSN : 1226-0657

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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: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
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. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 29(2), 179-188, https://doi.org/https://doi.org/10.7468/jksmeb.2022.29.2.179

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\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$</TEX> and <TEX>$$f\(\sum\limits_{i=1}^{l}x_i\)+\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 &#x2208; N, s, l &#x2265; 3) in quasi-Banach spaces.

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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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