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

• 论文 • 上一篇    下一篇

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

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

  1. 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   

  1. 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:

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
nk=2(∑ki1=2k+1i2=i1+1…∑nin−k+1=in−k+1)f (∑ni=1, i6=i1, …, ink+1xi −∑nk+1r=1xir)+ f (∑ni=1xi)= 2n−21≤i<jn
(f (xi + xj)+f (xi −  xj)−2n−5(n − 2)∑ni=1f (2xi)
(∈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:

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
nk=2(∑ki1=2k+1i2=i1+1…∑nin−k+1=in−k+1)f (∑ni=1, i6=i1, …, ink+1xi −∑nk+1r=1xir)+ f (∑ni=1xi)= 2n−21≤i<jn
(f (xi + xj)+f (xi −  xj)−2n−5(n − 2)∑ni=1f (2xi)
(∈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.

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