On the stability of generalized additive functional inequalities in Banach spaces

Choonkil Park, Jung Rye Lee, Dong Yun Shin

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We study the following generalized additive functional inequality ∥af(x) + bf(y) + cf(z)∥ ≤ ∥f(αx + βy + γz)∥, associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.

Original languageEnglish
Article number210626
JournalJournal of Inequalities and Applications
Volume2008
DOIs
StatePublished - 2008 Jun 24

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Additive Functional
Functional Inequalities
Banach spaces
Banach space
Hyers-Ulam-Rassias Stability

Cite this

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title = "On the stability of generalized additive functional inequalities in Banach spaces",
abstract = "We study the following generalized additive functional inequality ∥af(x) + bf(y) + cf(z)∥ ≤ ∥f(αx + βy + γz)∥, associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.",
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On the stability of generalized additive functional inequalities in Banach spaces. / Park, Choonkil; Lee, Jung Rye; Shin, Dong Yun.

In: Journal of Inequalities and Applications, Vol. 2008, 210626, 24.06.2008.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the stability of generalized additive functional inequalities in Banach spaces

AU - Park, Choonkil

AU - Lee, Jung Rye

AU - Shin, Dong Yun

PY - 2008/6/24

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N2 - We study the following generalized additive functional inequality ∥af(x) + bf(y) + cf(z)∥ ≤ ∥f(αx + βy + γz)∥, associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.

AB - We study the following generalized additive functional inequality ∥af(x) + bf(y) + cf(z)∥ ≤ ∥f(αx + βy + γz)∥, associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.

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DO - 10.1155/2008/210626

M3 - Article

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JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

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