The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ASYMPTOTIC BEHAVIORS OF JENSEN TYPE FUNCTIONAL EQUATIONS IN HALF PLANES

  • Received : 2010.11.06
  • Accepted : 2011.03.16
  • Published : 2011.05.31
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Abstract

Let f : ${\mathbb{R}}{\rightarrow}{\mathbb{C}}$. We consider the Hyers-Ulam stability of Jensen type functional inequality $$|f(px+qy)-Pf(x)-Qf(y)|{\leq}{\epsilon}$$ in the half planes {(x, y) : $kx+sy{\geq}d$} for fixed d, k, $s{\in}{\mathbb{R}}$ with $k{\neq}0$ or $s{\neq}0$. As consequences of the results we obtain the asymptotic behaviors of f satisfying $$|f(px+qy)-Pf(x)-Qf(y)|{\rightarrow}0$$ as $kx+sy{\rightarrow}{\infty}$.

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References

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