On the Stability of a Mixed Functional Equation Deriving from Additive, Quadratic and Cubic Mappings

被引：1

作者：

Li Guang WANG ^{[1
]}

Kun Peng XU ^{[2
]}

Qiu Wen LIU ^{[1
]}

机构：

[1] School of Mathematical Sciences, Qufu Normal University

[2] Zaozhuang Economics School

来源：

ActaMathematicaSinica(EnglishSeries) | 2014年 / 30卷 / 06期

关键词：

Additive mapping; quadratic mapping; cubic mapping; Hyers–Ulam stability;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the general solution and the Hyers–Ulam stability of the following mixed functional equation f(2x + y) + f(2x- y) = 2f(2x) + 2f(x + y) + 2f(x- y)- 4f(x)- f(y)- f(-y)deriving from additive, quadratic and cubic mappings on Banach spaces.

引用

页码：1033 / 1049

页数：17

共 9 条

[1] Generalized Hyers-Ulam Stability of a General Mixed Additive-cubic Functional Equation in Quasi-Banach Spaces [J].

Tian Zhou XU ;

John Michael RASSIAS ;

Wan Xin XU .

ActaMathematicaSinica, 2012, 28 (03) :529-560

[2]

The Hyers-Ulam stability of a functional equation deriving from quadratic and cubic functions in quasi- β -normed spaces[J] . Li Guang Wang,Bo Liu.Acta Mathematica Sinica, English Series . 2010 (12)

[3] Asymptotic aspect of the quadratic functional equation in multi-normed spaces [J].

Moslehian, M. S. ;

Nikodem, K. ;

Popa, D. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (02) :717-724

[4]

Generalization of Ulam stability problem for Euler–Lagrange quadratic mappings[J] . Hark-Mahn Kim,John Michael Rassias.Journal of Mathematical Analysis and Applications . 2007 (1)

[5] On a bi-quadratic functional equation and its stability [J].

Park, WG ;

Bae, JH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (04) :643-654

[6]

On the Hyers–Ulam–Rassias stability of generalized quadratic mappings in Banach modules[J] . Chun-Gil Park.Journal of Mathematical Analysis and Applications . 2003 (1)

[7]

The generalized Hyers–Ulam–Rassias stability of a cubic functional equation[J] . Kil-Woung Jun,Hark-Mahn Kim.Journal of Mathematical Analysis and Applications . 2002 (2)

[8] ON THE BEHAVIOR OF MAPPINGS WHICH DO NOT SATISFY HYERS-ULAM STABILITY [J].

RASSIAS, TM ;

SEMRL, P .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 114 (04) :989-993

[9]

On the stability of the linear mapping in Banach spaces[J] . Themistocles M. Rassias.Proceedings of the American Mathematical Society . 1978 (2)

← 1 →