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SEVERAL STABILITY PROBLEMS OF A QUADRATIC FUNCTIONAL EQUATION

Cho, In-Goo;Koh, Hee-Jeong

  • Received : 2010.01.18
  • Published : 2011.01.31

Abstract

In this paper, we investigate the stability using shadowing property in Abelian metric group and the generalized Hyers-Ulam-Rassias stability in Banach spaces of a quadratic functional equation, $f(x_1+x_2+x_3+x_4)+f(-x_1+x_2-x_3+x_4)+f(-x_1+x_2+x_3)+f(-x_2+x_3+x_4)+f(-x_3+x_4+x_1)+f(-x_4+x_1+x_2)=5{\sum\limits_{i=1}^4}f(x_i)$. Also, we study the stability using the alternative fixed point theory of the functional equation in Banach spaces.

Keywords

shadowing property-stability;generalized Hyers-Ulam stability;quadratic mapping

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Cited by

  1. On Some Recent Developments in Ulam's Type Stability vol.2012, 2012, https://doi.org/10.1155/2012/716936