Refined stability of an additive functional equation with several variables

2013 ◽  
Vol 7 ◽  
pp. 6251-6261
Author(s):  
Hark-Mahn Kim ◽  
Soon Lee
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Several Variables

scholarly journals Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias Stabilities of an Additive Functional Equation in Several Variables

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Paisan Nakmahachalasint
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Several Variables ◽  
Rassias Stability

It is well known that the concept of Hyers-Ulam-Rassias stability was originated by Th. M. Rassias (1978) and the concept of Ulam-Gavruta-Rassias stability was originated by J. M. Rassias (1982–1989) and by P. Găvruta (1999). In this paper, we give results concerning these two stabilities.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

scholarly journals Solutions and the Generalized Hyers-Ulam-Rassias Stability of a Generalized Quadratic-Additive Functional Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Janfada ◽  
R. Shourvazi
Keyword(s):  
Functional Equation ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
General Solutions ◽  
Rassias Stability

We study general solutions and generalized Hyers-Ulam-Rassias stability of the following -dimensional functional equation , , on non-Archimedean normed spaces.

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 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.

Sign in / Sign up

Export Citation Format

Share Document