scholarly journals A circulant functional equation for the additive function and its stability

2019 ◽  
Keyword(s):  
Functional Equation ◽  
Additive Function

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 A circulant functional equation for the additive function and its stability

2019 ◽  
Vol 43 (6) ◽  
pp. 2821-2832
Author(s):  
Vichian LAOHAKOSOL ◽  
Watcharapon PIMSERT ◽  
Kanet PONPETCH
Keyword(s):  
Functional Equation ◽  
Additive Function

scholarly journals The Functional Equation max{χ(xy),χ(xy-1)}=χ(x)χ(y) on Groups and Related Results

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 382
Author(s):  
Muhammad Sarfraz ◽  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Zero Solution ◽  
Research Paper ◽  
Factor Group ◽  
Normal Subgroups

This research paper focuses on the investigation of the solutions χ:G→R of the maximum functional equation max{χ(xy),χ(xy−1)}=χ(x)χ(y), for every x,y∈G, where G is any group. We determine that if a group G is divisible by two and three, then every non-zero solution is necessarily strictly positive; by the work of Toborg, we can then conclude that the solutions are exactly the e|α| for an additive function α:G→R. Moreover, our investigation yields reliable solutions to a functional equation on any group G, instead of being divisible by two and three. We also prove the existence of normal subgroups Zχ and Nχ of any group G that satisfy some properties, and any solution can be interpreted as a function on the abelian factor group G/Nχ.

scholarly journals On the Hyers-Ulam-Rassias Stability of a General Quintic Functional Equation and a General Sextic Functional Equation

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 510 ◽  
Author(s):  
Yang-Hi Lee
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Functional Equations ◽  
Quadratic Function ◽  
Rassias Stability

The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers–Ulam–Rassias stability of the general quintic functional equation and the general sextic functional equation.

The one-level functional equation of multi-rate loss systems

2003 ◽  
Vol 14 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Harro L. Hartmann ◽  
Martin Knoke
Keyword(s):  
Functional Equation ◽  
Loss Systems ◽  
The One ◽  
Rate Loss

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

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.

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