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Isomorphisms and Derivations in Proper JCQ*-Triples

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Functional Equations in Mathematical Analysis

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

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Abstract

We investigate homomorphisms in proper JCQ ∗-triples and derivations on proper JCQ ∗-triples associated with the 3-variable Jensen functional equation

$$\begin{array}{rcl} 2f\left (\frac{x + y + z} {2} \right ) = f(x) + f(y) + f(z)\;,& & \\ \end{array}$$

which was introduced and investigated by Park, Cho and Han. We moreover prove the Hyers–Ulam–Rassias stability of homomorphisms in proper JCQ ∗-triples and of derivations on proper JCQ ∗-triples. This is applied to investigate isomorphisms between proper JCQ ∗-triples.

Mathematics Subject Classification (2010): Primary 47Jxx, 39B52, 46B03, 17C65, 47B48, 47L60, 46L05

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Authors and Affiliations

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

    Choonkil Park

  2. Department of Mathematics, Semnan University, 35195-363, Semnan, Iran

    Madjid Eshaghi-Gordji

Authors
  1. Choonkil Park
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  2. Madjid Eshaghi-Gordji
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Correspondence to Madjid Eshaghi-Gordji .

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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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Park, C., Eshaghi-Gordji, M. (2011). Isomorphisms and Derivations in Proper JCQ*-Triples. 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_19

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