The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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STABILITY OF s-VARIABLE ADDITIVE AND l-VARIABLE QUADRATIC FUNCTIONAL EQUATIONS

  • Received : 2022.04.09
  • Accepted : 2022.04.28
  • Published : 2022.05.31
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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 $$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$$ and $$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)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

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References

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