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Generalized orthogonal stability of some functional equations

Abstract

We deal with a conditional functional inequality, where is a given orthogonality relation, is a given nonnegative number, and is a given real number. Under suitable assumptions, we prove that any solution of the above inequality has to be uniformly close to an orthogonally additive mapping, that is, satisfying the condition. In the sequel, we deal with some other functional inequalities and we also present some applications and generalizations of the first result.

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Correspondence to Justyna Sikorska.

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Sikorska, J. Generalized orthogonal stability of some functional equations. J Inequal Appl 2006, 12404 (2006). https://doi.org/10.1155/JIA/2006/12404

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Keywords

  • Real Number
  • Functional Equation
  • Additive Mapping
  • Orthogonality Relation
  • Suitable Assumption
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