APPROXIMATE 3-LIE HOMOMORPHISMS ON LIE ALGEBRA SYSTEMS

2013 ◽  
Vol 11 (05) ◽  
pp. 1350022
Author(s):  
ALI EBADIAN ◽  
RASOUL AGHALARY ◽  
JAVAD SHOKRI
Keyword(s):  
Functional Equation ◽  
Lie Algebra ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
Lie Systems ◽  
The Stability

We prove the generalized Hyers–Ulam stability of mapping on normed spaces for the following Jensen functional equation: [Formula: see text] Moreover, we investigate the stability of homomorphisms on normed 3-Lie systems.

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 the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

scholarly journals Intuitionistic fuzzy almost Cauchy–Jensen mappings

2016 ◽  
Vol 49 (1) ◽  
Author(s):  
M. E. Gordji ◽  
S. Abbaszadeh
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Intuitionistic Fuzzy ◽  
Jensen Functional Equation ◽  
Jensen Functional

AbstractIn this paper, we first investigate the Hyers–Ulam stability of the generalized Cauchy–Jensen functional equation of

scholarly journals On the Intuitionistic Fuzzy Stability of Ring Homomorphism and Ring Derivation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jaiok Roh ◽  
Ick-Soon Chang
Keyword(s):  
Functional Equation ◽  
Banach Algebra ◽  
Ring Homomorphism ◽  
Normed Algebra ◽  
Intuitionistic Fuzzy ◽  
Jensen Functional Equation ◽  
Jensen Functional ◽  
The Stability ◽  
Ring Derivation

We take into account the stability of ring homomorphism and ring derivation in intuitionistic fuzzy Banach algebra associated with the Jensen functional equation. In addition, we deal with the superstability of functional equationf(xy)=xf(y)+f(x)yin an intuitionistic fuzzy normed algebra with unit.

scholarly journals On the Stability of -Derivations and Lie -Algebra Homomorphisms on Lie -Algebras: A Fixed Points Method

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Points ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
The Stability ◽  
Algebra Homomorphisms ◽  
Stability Results

We investigate new generalized Hyers-Ulam stability results for -derivations and Lie -algebra homomorphisms on Lie -algebras associated with the additive functional equation:

scholarly journals On the stability problem of quadratic functional equations in 2-Banach spaces

2017 ◽  
pp. 5054-5061
Author(s):  
Seong Sik Kim ◽  
Ga Ya Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Stability Problem ◽  
Functional Equations ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability ◽  
Stability Results

In this paper, we investigate the stability problem in the spirit of Hyers-Ulam, Rassias and G·avruta for the quadratic functional equation:f(2x + y) + f(2x ¡ y) = 2f(x + y) + 2f(x ¡ y) + 4f(x) ¡ 2f(y) in 2-Banach spaces. These results extend the generalized Hyers-Ulam stability results by thequadratic functional equation in normed spaces to 2-Banach spaces.

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 Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

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