FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

被引：5

作者：

Kenary, H. Azadi ^{[1
]}

Zohdi, A. R. ^{[2
]}

Gordji, M. Eshaghi ^{[3
]}

机构：

[1] Islamic Azad Univ, Beyza Branch, Dept Math, Beyza, Iran

[2] Islamic Azad Univ, Marvdasht Branch, Dept Math, Marvdasht 7371113119, Iran

[3] Semnan Univ, Dept Math, Semnan, Iran

来源：

ACTA MATHEMATICA SCIENTIA | 2013年 / 33卷 / 04期

关键词：

generalized Hyers-Ulam stability; quartic functional equation; Banach module; unital Banach algebra; generalized metric space; fixed point method; HYERS-ULAM STABILITY; FUNCTIONAL-EQUATION; ADDITIVE MAPPINGS; RASSIAS STABILITY; SPACES;

D O I：

10.1016/S0252-9602(13)60067-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equation Sigma(n)(k=2)(Sigma(k)(i1=2) Sigma(i2=i1)+1(k+1) ...Sigma(in-k+1=in-k)+1(n) ) f (Sigma(i=1,i not equal i1),..,(n)(in-k+1) x(i) -Sigma(r=1) (n-k+1) x(ir)) + f(Sigma(i=1) x(i) (n)) (n is an element of N, n >= 3) in beta-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability (briefly, HUR-stability) originated from 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.

引用

页码：1113 / 1118

页数：6

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[J]. Acta Mathematica Scientia, 2013, 33 (04) : 1113 - 1118
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