scholarly journals Approximately Ternary Homomorphisms onC*-Ternary Algebras

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Eon Wha Shim ◽  
Su Min Kwon ◽  
Yun Tark Hyen ◽  
Yong Hun Choi ◽  
Abasalt Bodaghi
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Direct Method ◽  
Ulam Stability ◽  
Fixed Point Approach ◽  
Ternary Algebras

Gordji et al. established the Hyers-Ulam stability and the superstability ofC*-ternary homomorphisms andC*-ternary derivations onC*-ternary algebras, associated with the following functional equation:fx2-x1/3+fx1-3x3/3+f3x1+3x3-x2/3=fx1, by the direct method. Under the conditions in the main theorems, we can show that the related mappings must be zero. In this paper, we correct the conditions and prove the corrected theorems. Furthermore, we prove the Hyers-Ulam stability and the superstability ofC*-ternary homomorphisms andC*-ternary derivations onC*-ternary algebras by using a fixed point approach.

scholarly journals Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Azadi Kenary ◽  
H. Rezaei ◽  
Y. W. Lee ◽  
G. H. Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Functional Equations ◽  
Mixed Type ◽  
Direct Method ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Methods ◽  
Rassias Stability

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equationf(x+ky)+f(x−ky)=f(x+y)+f(x−y)+(2(k+1)/k)f(ky)−2(k+1)f(y)for fixed integerskwithk≠0,±1in fuzzy Banach spaces.

scholarly journals Nearly Ternary Quadratic Higher Derivations on Non-Archimedean Ternary Banach Algebras: A Fixed Point Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
J. M. Rassias ◽  
Badrkhan Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach Algebras ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Ternary Algebras ◽  
The Stability

We investigate the stability and superstability of ternary quadratic higher derivations in non-Archimedean ternary algebras by using a version of fixed point theorem via quadratic functional equation.

scholarly journals On a functional equation that has the quadratic-multiplicative property

2020 ◽  
Vol 18 (1) ◽  
pp. 837-845 ◽  
Author(s):  
Choonkil Park ◽  
Kandhasamy Tamilvanan ◽  
Ganapathy Balasubramanian ◽  
Batool Noori ◽  
Abbas Najati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Direct Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Multiplicative Property ◽  
Multiplicative Functional

Abstract In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation: \phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v)] by using the direct method and the fixed point method.

STABILITY OF J*-DERIVATIONS

2012 ◽  
Vol 09 (05) ◽  
pp. 1220009
Author(s):  
CHOONKIL PARK ◽  
JUNG RYE LEE ◽  
DONG YUN SHIN
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Direct Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability

Gordji et al. proved the Hyers–Ulam stability and the superstability of J*-derivations in J*-algebras for the generalized Jensen type functional equation [Formula: see text] by using direct method and by fixed point method. They only proved the theorems for the case r > 1. In this paper, we prove the Hyers–Ulam stability and the superstability of J*-derivations in J*-algebras for the case r ≠ 0 of the above generalized Jensen type functional equation by using direct method and by fixed point method under slightly different conditions.

scholarly journals The cubic ρ-functional equation in matrix non-Archimedean random normed spaces

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2643-2653
Author(s):  
Zhihua Wang ◽  
Chaozhu Hu
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Real Number ◽  
Direct Method ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Cubic Functional Equation ◽  
Random Normed Spaces

Using the direct method and fixed point method, we investigate the Hyers-Ulam stability of the following cubic ?-functional equation f(x+2y) + f(x-2y)- 2f(x+y)-2f(x-y)-12f(x) = ?(4f(x+y/2) + 4f(x-y/2)-f(x+y)-f(x-y)-6f(x)) in matrix non-Archimedean random normed spaces, where ? is a fixed real number with ? ? 2.

scholarly journals A fixed point approach to the fuzzy stability of an AQCQ-functional equation

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1833-1851 ◽  
Author(s):  
Choonkil Park ◽  
Dong Shin ◽  
Reza Saadati ◽  
Jung Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Stability Problems ◽  
Fixed Point Approach ◽  
Quartic Functional Equation

In [32, 33], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quadraticcubic-quartic functional equation f(x+2y)+f(x-2y)=4f(x+y)+4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y) (1) in fuzzy Banach spaces.

scholarly journals A Fixed Point Approach to the Stability of a General Mixed AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Tian Zhou Xu ◽  
John Michael Rassias ◽  
Wan Xin Xu
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Fixed Integer ◽  
Fixed Point Approach ◽  
Quartic Functional Equation ◽  
Fixed Point Methods ◽  
The Stability

Using the fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equationf(x+ky)+f(x−ky)=k2f(x+y)+k2f(x−y)+2(1−k2)f(x)+((k4−k2)/12)[f(2y)+f(−2y)−4f(y)−4f(−y)]for a fixed integerkwithk≠0,±1 in non-Archimedean normed spaces.

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