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Stability and Instability of an Apollonius-Type Functional Equation

Author

Listed:
  • Ponmana Selvan Arumugam

    (Department of Mathematics, Rajalakshmi Engineering College (Autonomous), Thandalam, Chennai 602 105, Tamil Nadu, India)

  • Won-Gil Park

    (Department of Mathematics Education, Mokwon University, Daejeon 35349, Republic of Korea)

  • Jaiok Roh

    (Ilsong College of Liberal Arts (Mathematics), Hallym University, Chuncheon 24252, Republic of Korea)

Abstract

For the inner product space, we have Appolonius’ identity. From this identity, Park and Th. M. Rassias induced and investigated the quadratic functional equation of the Apollonius type. And Park and Th. M. Rassias first introduced an Apollonius-type additive functional equation. In this work, we investigate an Apollonius-type additive functional equation in 2-normed spaces. We first investigate the stability of an Apollonius-type additive functional equation in 2-Banach spaces by using Hyers’ direct method. Then, we consider the instability of an Apollonius-type additive functional equation in 2-Banach spaces.

Suggested Citation

  • Ponmana Selvan Arumugam & Won-Gil Park & Jaiok Roh, 2024. "Stability and Instability of an Apollonius-Type Functional Equation," Mathematics, MDPI, vol. 12(14), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2274-:d:1439542
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    References listed on IDEAS

    as
    1. Nicole Brillouët-Belluot & Janusz Brzdęk & Krzysztof Ciepliński, 2012. "On Some Recent Developments in Ulam's Type Stability," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-41, December.
    2. Zbigniew Gajda, 1991. "On stability of additive mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-4, January.
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