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Approximate Ternary Jordan Homomorphisms on Banach Ternary Algebras

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Book cover Nonlinear Analysis

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

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Abstract

Let A and B be two Banach ternary algebras over ℝ or ℂ. A linear mapping H:(A,[ ] A )→(B,[ ] B ) is called a ternary Jordan homomorphism if H([xxx] A )=[H(x)H(x)H(x)] B for all x∈A. In this paper, we investigate ternary Jordan homomorphisms on Banach ternary algebras, associated with the following functional equation

$$f \biggl(\frac{x_1}{2}+x_2+x_3 \biggr)= \frac{1}{2}f(x_1)+f(x_2)+f(x_3). $$

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Author information

Authors and Affiliations

  1. Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

    Madjid Eshaghi Gordji & M. Bavand Savadkouhi

  2. Department of Mathematics, Urmia University, Urmia, Iran

    N. Ghobadipour & A. Ebadian

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

    Choonkil Park

Authors
  1. Madjid Eshaghi Gordji
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  2. N. Ghobadipour
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  3. A. Ebadian
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  4. M. Bavand Savadkouhi
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  5. Choonkil Park
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Corresponding author

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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Gordji, M.E., Ghobadipour, N., Ebadian, A., Savadkouhi, M.B., Park, C. (2012). Approximate Ternary Jordan Homomorphisms on Banach Ternary Algebras. 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_17

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