ON AN L∞-VERSION OF A PEXIDERIZED QUADRATIC FUNCTIONAL INEQUALITY

Chung, Jae-Young

• 투고 : 2011.01.31
• 심사 : 2011.02.28
• 발행 : 2011.03.25
• 8 1

초록

Let f, g, h, k : $\mathbb{R}^n{\rightarrow}\mathbb{C}$ be locally integrable functions. We deal with the $L^{\infty}$-version of the Hyers-Ulam stability of the quadratic functional inequality and the Pexiderized quadratic functional inequality $${\parallel}f(x + y) + f(x - y) -2f(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ $${\parallel}f(x + y) + g(x - y) -2h(x) - 2f(y){\parallel}_{L^{\infty}(\mathbb{R}^n)}\leq\varepsilon$$ based on the concept of linear functionals on the space of smooth functions with compact support.

키워드

quadratic functional equation;stability;locally integrable functions;heat kernel;almost everywhere sense

참고문헌

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