Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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HYERS{ULAM STABILITY OF FUNCTIONAL INEQUALITIES ASSOCIATED WITH CAUCHY MAPPINGS

  • Kim, Hark-Mahn (Department of Mathematics Chungnam National University) ;
  • Oh, Jeong-Ha (Department of Mathematics Chungnam National University)
  • Received : 2007.10.29
  • Published : 2007.12.31
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Abstract

In this paper, we investigate the generalized Hyers-Ulam stability of the functional inequality $$||af(x)+bf(y)+cf(z)||{\leq}||f(ax+by+cz))||+{\phi}(x,y,z)$$ associated with Cauchy additive mappings. As a result, we obtain that if a mapping satisfies the functional inequality with perturbing term which satisfies certain conditions then there exists a Cauchy additive mapping near the mapping.

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