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On the Generalized Hyers-Ulam-Rassias Stability for a FunctionalEquation of Two Types in p-Banach Spaces

Yong-Soo Jung|박규홍
경북대학교 자연과학대학 수학과|2008.03|Kyungpook Mathematical Journal|제48권 제1호|pp. 45-61

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참고문헌

키워드

stabilitycubic mapping; quadratic mappingquasi-normed spacesp-Banach spaces.
주제분류수학

초록

We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x + 3y) + 6f(x − y) + 12f(2y) = 2f(x − 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated essentially with the Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.

Abstract

We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x + 3y) + 6f(x − y) + 12f(2y) = 2f(x − 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated essentially with the Th. M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.

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관련 논문AI추천

Stability of a quadratic functional equation in quasi--Banach spacesAbbas Najati, Fridoun Moradlou대한수학회 · 대한수학회보2008 · 제45권 제3호Hyers-Ulam Stability of Jensen Functional Equation in p- Banach Spaces김학만, 손은영, 전길웅경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제3호On the Stability of a Quadratic Functional EquationJae-Hyeong Bae, Kil-Woung Jun, Soon-Mo Jung경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제3호Generalized Hyers-Ulam Stability of Some Cubic-quadratic-additive Type Functional EquationsSoon-Mo Jung, Yang-Hi Lee경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제1호Hyers-Ulam-Rassias stability of a quadratic-cubic-quartic functional equation이양희강원경기수학회 · 한국수학논문집2020 · 제28권 제2호On the Hyers-Ulam-Rassias Stability of a General Quartic Functional Equation이양희영남수학회 · East Asian Mathematical Journal2019 · 제35권 제3호

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