Acta mathematica scientia, Series B >
FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN -NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS
Received date: 2012-04-09
Online published: 2013-07-20
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=2∑k+1i2=i1+1…∑nin−k+1=in−k+1)f (∑ni=1, i6=i1, …, in−k+1xi −∑n−k+1r=1xir)+ f (∑ni=1xi)= 2n−2∑1≤i<j≤n
(f (xi + xj)+f (xi − xj)−2n−5(n − 2)∑ni=1f (2xi)
(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.
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 . DOI: 10.1016/S0252-9602(13)60067-3
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