$\beta$-齐性赋范空间中近似二次泛函不等式

Approximate Quadratic Functional Inequality in $\beta$-Homogeneous Normed Spaces

中文关键词:  $\beta$-齐性空间  广义Hyers-Ulam稳定性  二次泛函不等式

英文关键词:$\beta$-homogeneous space  generalized Hyers-Ulam stability  quadratic functional inequality

中文摘要:

      在$\beta$-齐性复Banach空间中利用直接法证明了二次泛函不等式的广义Hyers-Ulam稳定性.

英文摘要:

      Using the direct method, we investigate the generalized Hyers-Ulam stability of the following quadratic functional inequality $\|f(x-y)+f(y-z)+f(x-z)-3f(x)-3f(y)-3f(z)\|\leq \|f(x+y+z)\|$ in $\beta$-homogeneous complex Banach spaces.