Stability and Instability of an Apollonius-Type Functional Equation

Autor:	Ponmana Selvan Arumugam, Won-Gil Park, Jaiok Roh
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	stability instability apollonius-type functional equation 2-normed space 2-Banach space Mathematics QA1-939
Zdroj:	Mathematics, Vol 12, Iss 14, p 2274 (2024)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math12142274
Popis:	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.
Databáze:	Directory of Open Access Journals
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