Results 21 to 30 of about 505 (94)

On a functional equation that has the quadratic-multiplicative property

Open Mathematics, 2020
In this article, we obtain the general solution and prove the Hyers-Ulam stability of the following quadratic-multiplicative functional equation:ϕ(st−uv)+ϕ(sv+tu)=[ϕ(s)+ϕ(u)][ϕ(t)+ϕ(v)]\phi (st-uv)+\phi (sv+tu)={[}\phi (s)+\phi (u)]{[}\phi (t)+\phi (v ...
Park Choonkil, Tamilvanan Kandhasamy, Balasubramanian Ganapathy, Noori Batool, Najati Abbas   +4 more
doaj   +1 more source

Jensen's functional equation on the symmetric group $\bold{S_n}$

, 2011
Two natural extensions of Jensen's functional equation on the real line are the equations $f(xy)+f(xy^{-1}) = 2f(x)$ and $f(xy)+f(y^{-1}x) = 2f(x)$, where $f$ is a map from a multiplicative group $G$ into an abelian additive group $H$.
C.T. Ng, C.T. Ng, C.T. Ng, C.T. Ng, Công-Trình Lê, M. Suzuki, Trung-Hiêu Thái   +6 more
core   +1 more source

Wigner's theorem revisited

, 2012
In this paper, we give the general solution of the functional equation $$\big\{\|f(x)+f(y)\|,\|f(x)-f(y)\|\big\}=\big\{\|x+y\|,\|x-y\|\big\}\qquad(x,y\in X)$$ where $f:X\to Y$ and $X,Y$ are inner product spaces. Related equations are also considered. Our
Maksa, Gyula, Páles, Zsolt
core   +1 more source

Approximate Homomorphisms of Ternary Semigroups

, 2005
A mapping $f:(G_1,[ ]_1)\to (G_2,[ ]_2)$ between ternary semigroups will be called a ternary homomorphism if $f([xyz]_1)=[f(x)f(y)f(z)]_2$. In this paper, we prove the generalized Hyers--Ulam--Rassias stability of mappings of commutative semigroups into ...
A. Cayley, C. Baak, D.H. Hyers, D.H. Hyers, G.L. Forti, J. Baker, J. Sylvester, L. Székelyhidi, L. Takhtajan, L. Vainerman, M. Amyari, M. Kapranov, M. S. Moslehian, M.S. Moslehian, N. Bazunova, P. Găvruta, R. Kerner, S.A. Rusakov, S.M. Ulam, Th.M. Rassias, Th.M. Rassias, V. Abramov, Y.L. Daletskii   +22 more
core   +2 more sources

Stability and Superstability of a Linear Functional Equation on Restricted Domains

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper investigates the Hyers–Ulam stability and superstability of the functional equation f(x2 + yf(z)) = xf(x) + zf(y) for real‐valued functions f : R⟶R on some restricted subsets of R.
Abbas Najati, Mohammad Amin Tareeghee, Themistocles M. Rassias, Arnab Biswas   +3 more
wiley   +1 more source

Hyers–Ulam Stability of Mixed Quintic and Sextic Equations in Matrix‐Valued Non‐Archimedean Random Normed Spaces via Fixed Point Methods

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper establishes the Hyers–Ulam stability of mixed quintic and sextic functional equations within matrix non‐Archimedean random normed spaces. Using fixed‐point techniques, we derive conditions under which approximate solutions guarantee exact solutions, generalizing stability results to these structured probabilistic spaces.
Khalil Shahbazpour, Ali Ebadian, Ali Jabbari, A. M. Nagy   +3 more
wiley   +1 more source

The Cosine-Sine Functional Equation on Semigroups

Annales Mathematicae Silesianae, 2022
The primary object of study is the “cosine-sine” functional equation f(xy) = f(x)g(y)+g(x)f(y)+h(x)h(y) for unknown functions f, g, h : S → ℂ, where S is a semigroup.
Ebanks Bruce
doaj   +1 more source

Satbility of Ternary Homomorphisms via Generalized Jensen Equation

, 2005
In this paper, we establish the generalized Hyers--Ulam--Rassias stability of homomorphisms between ternary algebras associted to the generalized Jensen functional equation $r f(\frac{sx+ty}{r}) = s f(x) + t f(y)$.Comment: 12 ...
Moslehian, Mohammad Sal, Szekelyhidi, Laszlo   +1 more
core   +2 more sources

Hyers-Ulam stability of quadratic forms in 2-normed spaces

Demonstratio Mathematica, 2019
In this paper, we obtain Hyers-Ulam stability of the functional ...
Park Won-Gil, Bae Jae-Hyeong
doaj   +1 more source

A Variant of D’Alembert’s Functional Equation on Semigroups with Endomorphisms

Annales Mathematicae Silesianae, 2022
Let S be a semigroup, and let φ, ψ: S → S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation f(xϕ(y))+f(ψ(y)x)=2f(x)f(y),      x,y ∈ S,
Akkaoui Ahmed, El Fatini Mohamed, Fadli Brahim   +2 more
doaj   +1 more source