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On the Stability of an Additive and Quadratic Functional Equation

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Nonlinear Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 68))

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Abstract

In Park et al. (J. Chungcheong Math. Soc. 21:455–466, 2008) considered the following Jensen additive and quadratic type functional equation

$$2 f \biggl(\frac{x+y}{2} \biggr) + f \biggl( \frac{x-y}{2} \biggr ) + f \biggl(\frac{y-x}{2} \biggr) = f(x) + f(y) . $$

In this paper, we investigate the following additive and quadratic functional equation

$$ 2 f(x+y) + f(x-y) + f(y-x) = 3f(x) + f(-x) + 3f(y) + f(-y) . $$
(34.1)

Furthermore, we prove the generalized Hyers–Ulam stability of the functional equation (34.1) in Banach spaces.

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Authors and Affiliations

  1. Department of Mathematics, Hanyang University, Seoul, 133-791, Republic of Korea

    Choonkil Park

Authors
  1. Choonkil Park
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Correspondence to Choonkil Park .

Editor information

Editors and Affiliations

  1. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  2. Center for Applied Optimization, Dept. Industrial & Systems, University of Florida, Weil Hall 303, Gainesville, 32611-6595, Florida, USA

    Pando G. Georgiev

  3. , Department of Mathematics & Statistics, University of Victoria, Finnerty Road 3800, Victoria, V8W 3R4, British Columbia, Canada

    Hari M. Srivastava

Additional information

Dedicated to Professor Themistocles M. Rassias on the occasion of his 60th birthday.

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Park, C. (2012). On the Stability of an Additive and Quadratic Functional Equation. In: Pardalos, P., Georgiev, P., Srivastava, H. (eds) Nonlinear Analysis. Springer Optimization and Its Applications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3498-6_34

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