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

doi:10.1016/S0252-9602(13)60067-3

数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 1113-1118.doi: 10.1016/S0252-9602(13)60067-3

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

H. Azadi KENARY*|A.R. ZOHDI|M. Eshaghi GORDJI

Department of Mathematics, Beyza Branch, Islamic Azad University, Beyza, Iran； Department of Mathematics, Marvdasht Branch, Islamic Azad University, Marvdasht 73711-13119, Iran； Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran

收稿日期:2012-04-09 出版日期:2013-07-20 发布日期:2013-07-20
通讯作者: H. Azadi KENARY，h.azadikenary@gmail.com E-mail:h.azadikenary@gmail.com；madjid.eshaghi@gmail.com

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

H. Azadi KENARY*|A.R. ZOHDI|M. Eshaghi GORDJI

Department of Mathematics, Beyza Branch, Islamic Azad University, Beyza, Iran； Department of Mathematics, Marvdasht Branch, Islamic Azad University, Marvdasht 73711-13119, Iran； Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran

Received:2012-04-09 Online:2013-07-20 Published:2013-07-20
Contact: H. Azadi KENARY，h.azadikenary@gmail.com E-mail:h.azadikenary@gmail.com；madjid.eshaghi@gmail.com

摘要/Abstract

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
∑ⁿ_k₌₂(∑^k_i₁₌₂∑^k+1_i2=i1+1…∑ⁿ_in−k_+1=in−k+1)f (∑ⁿ_i_{=1, i6=i1}, …, _in−k+1x_i−∑^n−k+1_r=1x_ir)+ f (∑ⁿ_i₌₁x_i)= 2ⁿ⁻²∑_1≤i<j≤_n(f (x_i+ x_j)+f (x_i− x_j)−2ⁿ⁻⁵(n − 2)∑ⁿ_i₌₁f (2x_i)
(n ∈N, n ≥ 3) in β-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.

关键词: generalized Hyers-Ulam stability, quartic functional equation, Banach mod-ule, unital Banach algebra, generalized metric space, fixed point method

Abstract:

Key words: generalized Hyers-Ulam stability, quartic functional equation, Banach mod-ule, unital Banach algebra, generalized metric space, fixed point method

中图分类号:

39B82

H. Azadi KENARY, A.R. ZOHDI, M. Eshaghi GORDJI. FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN -NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS[J]. 数学物理学报(英文版), 2013, 33(4): 1113-1118.

H. Azadi KENARY, A.R. ZOHDI, M. Eshaghi GORDJI. FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN -NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS[J]. Acta mathematica scientia,Series B, 2013, 33(4): 1113-1118.

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

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

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