Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (3): 690-702.doi: 10.1016/S0252-9602(15)30014-X

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ON THE HYERS-ULAM STABILITY OF AN EQUATION CHARACTERIZING MULTI-QUADRATIC MAPPINGS

Krzysztof CIEPLINSKI1, Angelika SUROWCZYK2   

  1. 1. Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland;
    2. Lipnica Wielka 532, 34-483, Lipnica Wielka, Poland
  • Received:2014-07-23 Online:2015-05-01 Published:2015-05-01
  • Contact: Krzysztof CIEPLIŃSK E-mail:kc@up.krakow.pl

Abstract:

In this article, we prove, both in complete non-Archimedean normed spaces and in 2-Banach spaces, the generalized Hyers-Ulam stability of an equation characterizing multi-quadratic mappings. Our results generalize some known outcomes.

Key words: Multi-quadratic mapping, (generalized) Hyers-Ulam stability, the Jordana-von Neumann functional equation, direct method

CLC Number: 

  • 39B82
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