Additive s-functional inequality and hom-derivations in Banach algebras

被引：24

作者：

Park, Choonkil ^{[1
]}

Lee, Jung Rye ^{[2
]}

Zhang, Xiaohong ^{[3
,4
]}

机构：

[1] Hanyang Univ, Res Inst Nat Sci, Seoul 04763, South Korea

[2] Daejin Univ, Dept Math, Kyunggi 11159, South Korea

[3] Shaanxi Univ Sci & Technol, Dept Math, Sch Arts & Sci, Xian, Shaanxi, Peoples R China

[4] Shanghai Maritime Univ, Dept Math, Coll Arts & Sci, Shanghai, Peoples R China

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2019年 / 21卷 / 01期

关键词：

Hyers-Ulam stability; hom-derivation in Banach algebra; additive s-functional inequality; fixed point method; direct method; STABILITY; EQUATION;

D O I：

10.1007/s11784-018-0652-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce and solve the following additive s- functional inequality: f ( x + y) - f( x) - f( y) = s( f( x - y) - f( x) - f(- y)) where s is a fixed nonzero complex number with | s| < 1. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive s-functional inequality (0.1) in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of hom-derivations in complex Banach algebras.

引用

页数：14

共 31 条

[1] Hyers-Ulam stability of associated Laguerre differential equations in a subclass of analytic functions
Abdollahpour, M. R.
Aghayari, R.
Rassias, M. Th.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 437 (01) : 605 - 612
[2] [Anonymous], 2007, B IRANIAN MATH SOC
[3] [Anonymous], 1984, AEQUATIONES MATH
[4] [Anonymous], 2003, J. Inequalities Pure Appl.
[5] [Anonymous], 1996, Int. J. Math. Math. Sci, DOI DOI 10.1155/S0161171296000324
[6] Aoki T, 1950, J MATH SOC JAPAN, V2, P64, DOI DOI 10.2969/JMSJ/00210064
[7] Fixed point methods for the generalized stability of functional equations in a single variable
Cadariu, Liviu
Radu, Viorel
[J]. FIXED POINT THEORY AND APPLICATIONS, 2008, 2008 (1)
[8] Cdariu L, 2004, GRAZER MATH BER, V346
[9] On the generalized stability of d'Alembert functional equation
Chahbi, Abdellatif
Bounader, Nordine
[J]. JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2013, 6 (03): : 198 - 204
[10] A FIXED POINT THEOREM OF ALTERNATIVE FOR CONTRACTIONS ON A GENERALIZED COMPLETE METRIC SPACE
DIAZ, JB
MARGOLIS, B
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 74 (02) : 305 - &

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