Stability and Instability of an Apollonius-Type Functional Equation

Ponmana Selvan Arumugam, Won-Gil Park and Jaiok Roh ()
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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

Mathematics, 2024, vol. 12, issue 14, 1-11

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.

Keywords: stability; instability; apollonius-type functional equation; 2-normed space; 2-Banach space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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