Additive functional inequalities in 2-Banach spaces

被引：0

作者：

Choonkil Park

机构：

[1] Research Institute for Natural Sciences,Department of Mathematics

[2] Hanyang University,undefined

来源：

Journal of Inequalities and Applications | / 2013卷

关键词：

Hyers-Ulam stability; linear 2-normed space; additive mapping; additive functional inequality; superstability;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove the Hyers-Ulam stability of the Cauchy functional inequality and theCauchy-Jensen functional inequality in 2-Banach spaces.

引用

共 14 条

[1]

Hyers DH(1941)On the stability of the linear functional equation Proc. Natl. Acad. Sci. USA 27 222-224

[2]

Aoki T(1950)On the stability of the linear transformation in Banach spaces J. Math. Soc. Jpn 2 64-66

[3]

Rassias TM(1978)On the stability of the linear mapping in Banach spaces Proc. Am. Math. Soc 72 297-300

[4]

Gǎvruta P(1994)A generalization of the Hyers-Ulam-Rassias stability of approximatelyadditive mappings J. Math. Anal. Appl 184 431-436

[5]

Gähler S(1963)2-metrische Räume und ihre topologische Struktur Math. Nachr 26 115-148

[6]

Gähler S(1964)Lineare 2-normierte Räumen Math. Nachr 28 1-43

[7]

White A(1969)2-Banach spaces Math. Nachr 42 43-60

[8]

Park W(2011)Approximate additive mappings in 2-Banach spaces and related topics J. Math. Anal. Appl 376 193-202

[9]

Eskandani GZ(2012)Hyers-Ulam-Rassias stability of Pexiderized Cauchy functional equation in2-Banach spaces J. Nonlinear Sci. Appl 5 459-465

[10]

Gǎvruta P(2001)Eine zur Parallelogrammgleichung äquivalente Ungleichung Aequ. Math 62 303-309