Abstract.
Using the fixed point alternative theorem we establish the orthogonal stability of the quadratic functional equation of Pexider type f (x+y)+g(x−y) = h(x)+k(y), where f, g, h, k are mappings from a symmetric orthogonality space to a Banach space, by orthogonal additive mappings under a necessary and sufficient condition on f.
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Mirzavaziri, M., Moslehian, M.S. A fixed point approach to stability of a quadratic equation. Bull Braz Math Soc, New Series 37, 361–376 (2006). https://doi.org/10.1007/s00574-006-0016-z
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DOI: https://doi.org/10.1007/s00574-006-0016-z
Keywords:
- orthogonal stability
- Pexiderized quadratic equation
- orthogonally quadratic mapping
- quadratic mapping
- orthogonally additive mapping
- additive mapping
- orthogonality space
- fixed point alternative theorem