On the stability problem of quadratic functional equations in 2-Banach spaces

  • Seong Sik Kim Department of Mathematics, Dongeui University Busan 614-714, Korea
  • Ga Ya Kim Department of Urban Engineering, Dongeui University Busan 614-714, Korea
  • Soo Hwan Kim Department of Mathematics, Dongeui University Busan 614-714, Korea

Abstract

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and G·avruta for the quadratic functional equation:
f(2x + y) + f(2x ¡ y) = 2f(x + y) + 2f(x ¡ y) + 4f(x) ¡ 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by the
quadratic functional equation in normed spaces to 2-Banach spaces.

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Published
2017-10-01
Section
Articles