scholarly journals On the Stability of Alternative Additive Equations in Multi-β-Normed Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Xiuzhong Yang ◽  
Jing Ma ◽  
Guofen Liu
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
The Stability

We introduce the notion of multi-β-normed space (0<β≤1) and study the stability of the alternative additive functional equation of two forms in this type of space.

The stability of an additive functional equation in menger probabilistic φ-normed spaces

2011 ◽  
Vol 61 (5) ◽  
Author(s):  
D. Miheţ ◽  
R. Saadati ◽  
S. Vaezpour
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Stability Result ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
The Stability

AbstractWe establish a stability result concerning the functional equation: $\sum\limits_{i = 1}^m {f\left( {mx_i + \sum\limits_{j = 1,j \ne i}^m {x_j } } \right) + f\left( {\sum\limits_{i = 1}^m {x_i } } \right) = 2f\left( {\sum\limits_{i = 1}^m {mx_i } } \right)} $ in a large class of complete probabilistic normed spaces, via fixed point theory.

On the stability of some functional equations in Menger φ-normed spaces

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Dorel Miheţ ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
The Stability ◽  
Stability Results

AbstractRecently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

scholarly journals Fuzzy approximation of an additive functional equation

2011 ◽  
Vol 9 (2) ◽  
pp. 205-215 ◽  
Author(s):  
G. Zamani Eskandani ◽  
Ali Reza Zamani ◽  
H. Vaezi
Keyword(s):  
Banach Space ◽  
Functional Equation ◽  
Banach Spaces ◽  
Normed Space ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Fuzzy Approximation ◽  
The Stability ◽  
Rassias Stability

In this paper, we investigate the generalized Hyers– Ulam– Rassias stability of the functional equation∑i=1mf(mxi+∑j=1, j≠imxj)+f(∑i=1mxi)=2f(∑i=1mmxi)in fuzzy Banach spaces and some applications of our results in the stability of above mapping from a normed space to a Banach space will be exhibited.

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 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 Stability of a Bi-Additive Functional Equation in Banach Modules Over aC⋆-Algebra

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Won-Gil Park ◽  
Jae-Hyeong Bae
Keyword(s):  
Functional Equation ◽  
Borel Function ◽  
Additive Functional ◽  
Additive Functional Equation ◽  
Banach Modules ◽  
The Stability

We solve the bi-additive functional equationf(x+y,z−w)+f(x−y,z+w)=2f(x,z)−2f(y,w)and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unitalC⋆-algebra.

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