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Generalized Hyers–Ulam Stability for General Quadratic Functional Equation in Quasi-Banach Spaces

Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 52)

Abstract

In this paper, we investigate the generalized Hyers–Ulam stability of an n-dimensional quadratic functional equation
$$f\bigg{(}\sum \limits_{i=1}^{n}{x}_{ i}\bigg{)} +{ \sum \nolimits }_{1\leq i<j\leq n}f({x}_{i} - {x}_{j}) = n\sum \limits_{i=1}^{n}f({x}_{ i})\qquad (n \geq 2)$$
in quasi-Banach spaces.

Keywords

Stability Functional equations Quasi-Banach space Quadratic function 

Notes

Acknowledgements

I would like to express my sincere gratitude to Professor Ding Guanggui for his guidance and convey my heartfelt thanks to Professor Themistocles M.Rassias for his valuable comments.

The author was supported in part by Research Foundation for Doctor Programme (Grant No. 20060055010) and National Natural Science Foundation of China (Grant No. 10871101).

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsQingao UniversityQingdaoChina
  2. 2.Department of MathematicsNankai UniversityTianjinChina

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