• Title/Summary/Keyword: almost everywhere sense

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STABILITY OF TRIGONOMETRIC TYPE FUNCTIONAL EQUATIONS IN RESTRICTED DOMAINS

  • Chung, Jae-Young
    • The Pure and Applied Mathematics
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    • v.18 no.3
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    • pp.231-244
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    • 2011
  • We prove the Hyers-Ulam stability for trigonometric type functional inequalities in restricted domains with time variables. As consequences of the result we obtain asymptotic behaviors of the inequalities and stability of related functional inequalities in almost everywhere sense.

ON AN L-VERSION OF A PEXIDERIZED QUADRATIC FUNCTIONAL INEQUALITY

  • Chung, Jae-Young
    • Honam Mathematical Journal
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    • v.33 no.1
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    • pp.73-84
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    • 2011
  • 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.