Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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STABILITY OF THE MULTI-JENSEN EQUATION

  • Prager, Wolfgang (INSTITUT FUR MATHEMATIK AND WISSENSCHAFTLICHES RECHNEN KARL-FRANZENS UNIVERSITY GRAZ) ;
  • Schwaiger, Jens (INSTITUT FUR MATHEMATIK AND WISSENSCHAFTLICHES RECHNEN KARL-FRANZENS UNIVERSITY GRAZ)
  • Published : 2008.02.29
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Abstract

Given an $m{\in}\mathbb{N}$ and two vector spaces V and W, a function f : $V^m{\rightarrow}W$ is called multi-Jensen if it satisfies Jensen's equation in each variable separately. In this paper we unify these m Jensen equations to obtain a single functional equation for f and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.

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References

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  3. G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), no. 1-2, 143-190 https://doi.org/10.1007/BF01831117
  4. W. Prager and J. Schwaiger, Multi-affine and multi-Jensen functions and their connection with generalized polynomials, Aequationes Math. 69 (2005), no. 1-2, 41-57 https://doi.org/10.1007/s00010-004-2756-4

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