Stability and Instability of an Apollonius-Type Functional Equation

被引：0

作者：

Arumugam, Ponmana Selvan ^{[1
]}

Park, Won-Gil ^{[2
]}

Roh, Jaiok ^{[3
]}

机构：

[1] Rajalakshmi Engn Coll Autonomous, Dept Math, Chennai 602105, Tamil Nadu, India

[2] Mokwon Univ, Dept Math Educ, Daejeon 302318, South Korea

[3] Hallym Univ, Ilsong Coll Liberal Arts Math, Chunchon 24252, South Korea

来源：

MATHEMATICS | 2024年 / 12卷 / 14期

基金：

新加坡国家研究基金会;

关键词：

stability; instability; apollonius-type functional equation; 2-normed space; 2-Banach space; HYERS-ULAM STABILITY;

D O I：

10.3390/math12142274

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：11

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