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An Additive Functional Equation in Orthogonality Spaces

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Abstract

By applying the fixed point method as well as the direct method, we provide a proof of the Hyers-Ulam stability of linear mappings, isometric linear mappings and 2-isometric linear mappings in Banach modules over a unital C ∗-algebra and in non-Archimedean Banach modules over a unital C ∗-algebra associated with an orthogonally additive functional equation. Moreover, we prove the Hyers-Ulam stability of homomorphisms in C ∗-algebras associated with an orthogonally additive functional equation.

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Authors and Affiliations

  1. Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, 133-791, South Korea

    Choonkil Park

  2. Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Themistocles M. Rassias

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  1. Choonkil Park
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  2. Themistocles M. Rassias
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Correspondence to Choonkil Park .

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Editors and Affiliations

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

    Panos M. Pardalos

  2. , Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens, 15780, Greece

    Themistocles M. Rassias

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Dedicated to the 80th Anniversary of Professor Stephen Smale

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Park, C., Rassias, T.M. (2012). An Additive Functional Equation in Orthogonality Spaces. In: Pardalos, P., Rassias, T. (eds) Essays in Mathematics and its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28821-0_14

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