scholarly journals Generalized Hyers-Ulam stability for general additive functional equations on non-Archimedean random lie C*-algebras

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2127-2138
Author(s):  
Zhihua Wang ◽  
Prasanna Sahoo

In this paper, using the fixed point method, we prove some results related to the generalized Hyers-Ulam stability of homomorphisms and derivations in non-Archimedean random C*-algebras and non-Archimedean random Lie C*-algebras for the generalized additive functional equation ?1 ? i < j ?n f(xi+xj/2 + ?n-2 l=1,kl?i,j xkl) = (n-1)2/2 ?n,i=1 f(xi) where n ? N is a fixed integer with n ? 3.

2018 ◽  
Vol 51 (1) ◽  
pp. 37-44 ◽  
Author(s):  
Zhihua Wang ◽  
Reza Saadati

AbstractIn this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation,where m ≥ 2.


2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Fridoun Moradlou ◽  
Hamid Vaezi ◽  
Choonkil Park

Using the fixed point method, we prove the generalized Hyers-Ulam stability ofC∗-algebra homomorphisms and of generalized derivations onC∗-algebras for the following functional equation of Apollonius type∑i=1nf(z−xi)=−(1/n)∑1≤i<j≤nf(xi+xj)+nf(z−(1/n2)∑i=1nxi).


2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yeol Je Cho ◽  
Reza Saadati ◽  
Javad Vahidi

Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms inC∗-algebras and LieC∗-algebras and of derivations on non-ArchimedeanC∗-algebras and Non-Archimedean LieC∗-algebras for anm-variable additive functional equation.


Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1833-1851 ◽  
Author(s):  
Choonkil Park ◽  
Dong Shin ◽  
Reza Saadati ◽  
Jung Lee

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.


2013 ◽  
Vol 10 (04) ◽  
pp. 1320001
Author(s):  
CHOONKIL PARK

Park and Rassias proved the superstability of C*-ternary homomorphisms, C*-ternary derivations, JB*-triple homomorphisms and JB*-triple derivations, associated with the following Apollonius type additive functional equation [Formula: see text] by using direct method. Under the conditions of the theorems, we can show that the mappings f must be zero. In this paper, we correct the conditions. Furthermore, we prove the superstability of C*-ternary homomorphisms, C*-ternary derivations, JB*-triple homomorphisms and JB*-triple derivations by using fixed point method.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Murali Ramdoss ◽  
Divyakumari Pachaiyappan ◽  
Choonkil Park ◽  
Jung Rye Lee

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.


2012 ◽  
Vol 2012 ◽  
pp. 1-45 ◽  
Author(s):  
Yeol Je Cho ◽  
Shin Min Kang ◽  
Reza Saadati

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 various complete random normed spaces.


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