scholarly journals Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Topological Structure ◽  
Continued Fraction ◽  
Additive Functional ◽  
Analytic Structure ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Analytical Structure ◽  
Knots And Links

We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation fx⊕y=fx⊕fy in tangle space which is a set of real tangles with analytic structure and describe the DNA recombination as the action of some enzymes on tangle space.

scholarly journals Hyers-Ulam stability of a finite variable mixed type quadratic-additive functional equation in quasi-Banach spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 5993-6005 ◽  
Author(s):  
K. Tamilvanan ◽  
◽  
Jung Rye Lee ◽  
Choonkil Park ◽  
◽  
...  
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Mixed Type ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation

scholarly journals Generalized Hyers–Ulam Stability of the Additive Functional Equation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 76 ◽  
Author(s):  
Yang-Hi Lee ◽  
Gwang Kim
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Additive Functional ◽  
Stability Theorem ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Stability Theorems ◽  
The Stability

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations.

scholarly journals Local stability of the additive functional equation and its applications

2003 ◽  
Vol 2003 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Soon-Mo Jung ◽  
Byungbae Kim
Keyword(s):  
Functional Equation ◽  
Large Class ◽  
Local Stability ◽  
Unbounded Domains ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Jensen’S Functional Equation ◽  
Restricted Domains ◽  
The Stability

The main purpose of this paper is to prove the Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen's functional equation for a large class of restricted domains.

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 Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
K. Tamilvanan ◽  
G. Balasubramanian ◽  
Nazek Alessa ◽  
K. Loganathan
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Nonnegative Integer ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Stability Results

In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ ∑ g = 1 l v g = ∑ 1 ≤ g < h < i ≤ l χ v g + v h + v i − ∑ 1 ≤ g < h ≤ l χ v g + v h − l 2 − 5 l + 2 / 2 ∑ g = 1 l χ v g − χ − v g / 2 . where l is a nonnegative integer with ℕ − 0,1,2,3,4 in Banach spaces.

scholarly journals Fuzzy Stability Results of Finite Variable Additive Functional Equation: Direct and Fixed Point Methods

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1050 ◽  
Author(s):  
Abdulaziz M. Alanazi ◽  
G. Muhiuddin ◽  
K. Tamilvanan ◽  
Ebtehaj N. Alenze ◽  
Abdelhalim Ebaid ◽  
...  
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Normed Space ◽  
Additive Functional ◽  
Current Work ◽  
Ulam Stability ◽  
Fuzzy Normed Space ◽  
Additive Functional Equation ◽  
Fixed Point Methods ◽  
Stability Results

In this current work, we introduce the finite variable additive functional equation and we derive its solution. In fact, we investigate the Hyers–Ulam stability results for the finite variable additive functional equation in fuzzy normed space by two different approaches of direct and fixed point methods.

Homomorphisms and derivations on C∗-ternary algebras associated with a generalized Cauchy-Jensen type additive functional equation

2014 ◽  
Vol 4 (3) ◽  
pp. 662-668
Author(s):  
Soo Hwan Kim ◽  
Seong Sik Kim ◽  
John Michael Rassias
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Ulam Stability ◽  
Fixed Integer ◽  
Additive Functional Equation ◽  
Ternary Algebras

In this paper, we prove the generalized Hyers-Ulam stability of C∗-ternary homomorphisms and C∗-ternary derivations on C∗-ternary algebras associated with the generalized Cauchy-Jensen type additive functional equationfor all xi; xj ∈ X where n ∈ Z+ is a fixed integer with n ≥ 3.ABSTRACTIn this paper, we prove the generalized Hyers-Ulam stability of ∁*-ternary homomorphisms and ∁*-ternary derivations on∁*-ternary algebras associated with the generalized Cauchy-Jensen type additive functional equation for all  where  is a fixed integer with

scholarly journals Fixed Points and Stability of an Additive Functional Equation ofn-Apollonius Type inC∗-Algebras

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Fridoun Moradlou ◽  
Hamid Vaezi ◽  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Additive Functional ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Generalized Derivations ◽  
Additive Functional Equation ◽  
Algebra Homomorphisms

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).

On approximate $\sigma$-homomorphisms and derivations on $C^*$-ternary

2015 ◽  
Vol 11 (3) ◽  
pp. 3114-3120
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Ternary Algebras

In this paper, we prove the generalized Hyers-Ulam stability of $\sigma$-homomorphisms and derivations on $C^*$-ternary algebras associated with the generalized Cauchy-Jensen type additive functional equation\begin{equation*}\sum_{i=1}^n f\left(x_i +{1 \over n-1}\sum_{j=1, j \ne i}^n x_j\right) =2 \sum_{i=1}^n f(x_i) \end{equation*}where $n \in \Z^+$ is a fixed integers with $n \ge 2$.

scholarly journals A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Uniqueness Theorem ◽  
Functional Equations ◽  
Additive Functional ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Additive Type ◽  
Stability Of Functional Equations ◽  
The Stability

We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functional equations. This uniqueness theorem can replace the repeated proofs for uniqueness of the relevant solutions of given equations while we investigate the stability of functional equations.

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