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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.18 No.2

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ASYMPTOTIC BEHAVIORS OF JENSEN TYPE FUNCTIONAL EQUATIONS IN HALF PLANES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2011, v.18 no.2, pp.113-128
https://doi.org/10.7468/jksmeb.2011.18.2.113
Kim, Sang-Youp
Kim, Gyu-Tae
Lee, Gi-Hui
Lee, Jae-Ho
Park, Gwang-Hyun
Kim,, S. , Kim,, G. , Lee,, G. , Lee,, J. , & Park,, G. (2011). ASYMPTOTIC BEHAVIORS OF JENSEN TYPE FUNCTIONAL EQUATIONS IN HALF PLANES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 18(2), 113-128, https://doi.org/10.7468/jksmeb.2011.18.2.113

Abstract

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

keywords
Hyers-Ulam stability, Jensen type functional equation, Pexider equation

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