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

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Functional Equations in Mathematical Analysis

Part of the book series: Springer Optimization and Its Applications ((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.

Mathematics Subject Classification(2000): Primary 39B52, 39B72

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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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Authors and Affiliations

  1. Department of Mathematics, Qingao University, Qingdao, 266071, China

    Jinmei Gao

  2. Department of Mathematics, Nankai University, Tianjin, 300071, China

    Jinmei Gao

Authors
  1. Jinmei Gao
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Correspondence to Jinmei Gao .

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Editors and Affiliations

  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

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Gao, J. (2011). Generalized Hyers–Ulam Stability for General Quadratic Functional Equation in Quasi-Banach Spaces. 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_10

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