Abstract
We prove a stability theorem for the quadratic functional equation
where G is an abelian group and σ is an involution of G. We also prove that for functions f from G to an inner product space E, the inequality
implies that f is a solution to the equation.
Mathematics Subject Classification (2000): Primary 39B52, 39B82
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Acknowledgements
Special thanks to Professor Janusz Brzdȩk for reading a preliminary version of the paper.
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Elqorachi, E., Manar, Y., Rassias, T.M. (2011). Hyers–Ulam Stability of the Quadratic Functional Equation. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_8
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DOI: https://doi.org/10.1007/978-1-4614-0055-4_8
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