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Stability Problem for Jensen–type Functional Equations of Cubic Mappings

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Abstract

In this paper, we establish the general solution and the generalized Hyers–Ulam–Rassias stability problem for a cubic Jensen–type functional equation,

$$ \begin{aligned} & 4f{\left( {\frac{{3x + y}} {4}} \right)} + 4f{\left( {\frac{{x + 3y}} {4}} \right)} = 6f{\left( {\frac{{x + y}} {2}} \right)} + f{\left( x \right)} + f{\left( y \right)}, \\ & 9f{\left( {\frac{{2x + y}} {3}} \right)} + 9f{\left( {\frac{{x + 2y}} {3}} \right)} = 16f{\left( {\frac{{x + y}} {2}} \right)} + f{\left( x \right)} + f{\left( y \right)} \\ \end{aligned} $$

in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Găvruta.

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Authors and Affiliations

  1. Department of Mathematics, Chungnam National University, 220 Yuseong-Gu, Daejeon, 305–764, Republic of Korea

    Kil-Woung Jun & Hark-Mahn Kim

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  1. Kil-Woung Jun
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  2. Hark-Mahn Kim
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Correspondence to Hark-Mahn Kim.

Additional information

This work is supported by the Korea Research Foundation Grant funded by the Korea Government (MOEHRD) (KRF–2005–070–C00009)

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Jun, KW., Kim, HM. Stability Problem for Jensen–type Functional Equations of Cubic Mappings. Acta Math Sinica 22, 1781–1788 (2006). https://doi.org/10.1007/s10114-005-0736-9

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