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The Hyers-Ulam stability of a quadratic functional equation with involution in paranormed spaces

김창일|신창협
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.03|한국수학논문집 (Korean Journal of Mathematics)|제24권 제1호|pp. 41-49|DOI http://dx.doi.org/10.11568/kjm.2016.24.1.41

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키워드

involutionfixed point methodquadratic functional equationparanormed space
주제분류수학

초록

In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation \begin{eqnarray*} & &f(x+y+z)+f(\sigma(x)+y+z)+f(x+\sigma(y)+z)+f(x+y+\sigma(z))\\ &=&4f(x)+4f(y)+4f(z) \end{eqnarray*} with involution in paranormed spaces.

Abstract

In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation \begin{eqnarray*} & &f(x+y+z)+f(\sigma(x)+y+z)+f(x+\sigma(y)+z)+f(x+y+\sigma(z))\\ &=&4f(x)+4f(y)+4f(z) \end{eqnarray*} with involution in paranormed spaces.

참고문헌 (19)

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