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http://dx.doi.org/10.7468/jksmeb.2011.18.2.113

ASYMPTOTIC BEHAVIORS OF JENSEN TYPE FUNCTIONAL EQUATIONS IN HALF PLANES  

Kim, Sang-Youp (Mathematics Group, Hong-Chun High School)
Kim, Gyu-Tae (Mathematics Group, Hong-Chun High School)
Lee, Gi-Hui (Mathematics Group, Hong-Chun High School)
Lee, Jae-Ho (Mathematics Group, Hong-Chun High School)
Park, Gwang-Hyun (Mathematics Group, Hong-Chun High School)
Publication Information
The Pure and Applied Mathematics / v.18, no.2, 2011 , pp. 113-128 More about this Journal
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 $kx+sy{\rightarrow}{\infty}$.
Keywords
Hyers-Ulam stability; Jensen type functional equation; Pexider equation;
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