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.

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

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 A general fixed point method for the stability of the monomial functional equation

2012 ◽  
Vol 28 (1) ◽  
pp. 25-36
Author(s):  
LIVIU CADARIU ◽  
◽  
VIOREL RADU ◽  
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Method ◽  
Point Method ◽  
Normed Spaces ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Error Estimations ◽  
The Stability ◽  
Stability Results

In this paper, we extend the ideas in [Cadariu, L. and Radu, V., ˘ A general fixed point method for the stability of Jensen functional equation, Bull. S¸ t. Univ. Politehnica Timis¸oara, Ser. Mat.-Fiz. 51(65) (2006), No. 2, 63–72] to obtain some general stability results for monomial functional equations in β−normed spaces. The fixed point alternative together the error estimations for generalized contractions of type Bianchini-Grandolfi are pointed out, and then used as fundamental tool. Some applications and examples which emphasize the very general hypotheses, are also given.

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.

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