WITHDRAWN: Stability of the Cauchy–Jensen functional equation in C∗-algebras: A fixed point approach

2007 ◽  
Author(s):  
Choonkil Park ◽  
Myoung-Jung Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
C Algebras ◽  
Fixed Point Approach ◽  
Jensen Functional Equation ◽  
Jensen Functional

scholarly journals A Fixed Point Approach to the Stability of a Cauchy-Jensen Functional Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jae-Hyeong Bae ◽  
Won-Gil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Fixed Point Approach ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Stability

We find out the general solution of a generalized Cauchy-Jensen functional equation and prove its stability. In fact, we investigate the existence of a Cauchy-Jensen mapping related to the generalized Cauchy-Jensen functional equation and prove its uniqueness. In the last section of this paper, we treat a fixed point approach to the stability of the Cauchy-Jensen functional equation.

ON APPROXIMATE n-ARY DERIVATIONS

2011 ◽  
Vol 08 (03) ◽  
pp. 485-500 ◽  
Author(s):  
M. ESHAGHI GORDJI ◽  
R. KHODABAKHSH ◽  
H. KHODAEI
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Algebras ◽  
C Algebras ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Ternary Algebras ◽  
Fixed Point Methods ◽  
The Stability

C. Park et al. proved the stability of homomorphisms and derivations in Banach algebras, Banach ternary algebras, C*-algebras, Lie C*-algebras and C*-ternary algebras. In this paper, we improve and generalize some results concerning derivations. We first introduce the following generalized Jensen functional equation [Formula: see text] and using fixed point methods, we prove the stability of n-ary derivations and n-ary Jordan derivations in n-ary Banach algebras. Secondly, we study this functional equation with *-n-ary derivations in C*-n-ary algebras.

scholarly journals Approximate -Lie Homomorphisms and Jordan -Lie Homomorphisms on -Lie Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
M. Eshaghi Gordji ◽  
G. H. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Lie Algebras ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Fixed Point Methods ◽  
The Stability

Using fixed point methods, we establish the stability of -Lie homomorphisms and Jordan -Lie homomorphisms on -Lie algebras associated to the following generalized Jensen functional equation .

scholarly journals Brzdęk’s fixed point method for the generalised hyperstability of bi-Jensen functional equation in (2,β)-Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4897-4910
Author(s):  
Iz-Iddine El-Fassi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Method ◽  
Point Method ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Fixed Point Theorem

Using the fixed point theorem [12, Theorem 1] in (2,?)-Banach spaces, we prove the generalized hyperstability results of the bi-Jensen functional equation 4f(x + z/2; y + w/2) = f (x,y) + f (x,w) + f (z,y) + f (y,w). Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. The method we use here can be applied to various similar equations in many variables.

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