Results 31 to 40 of about 120 (95)

On Approximations of a System of Functional Equations Having Monomials

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
We use an s‐monomial to define the multimonomial mappings as a system of functional equations having monomials. The main contribution of the paper is twofold. First, we give a representation of such new multiple variable mappings as a unified equation, thereby providing a complete characterization.
Siriluk Donganont, Abasalt Bodaghi, Xuping Zhang   +2 more
wiley   +1 more source

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

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

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

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

A fixed point approach to the hyers-ulam stability of a functional equation in various normed spaces [PDF]

, 2011
Using direct method, Kenary (Acta Universitatis Apulensis, to appear) proved the Hyers-Ulam stability of the following functional equation f (
Sun Jang, Hassan Azadi Kenary, Hassan Kenary, Sun Young Jang, Choonkil Park   +4 more
core   +1 more source

Comment on "on the stability of quadratic double centralizers and quadratic multipliers: a fixed point approach" [Bodaghi et al., j. inequal. appl. 2011, article id 957541 (2011)] [PDF]

, 2011
Bodaghi et al. [On the stability of quadratic double centralizers and quadratic multipliers: a fixed point approach. J. Inequal. Appl. 2011, Article ID 957541, 9pp.
Dong Yun Shin, Jung lee, Madjid Eshaghi Gordji, Choonkil Park, Jung Rye lee, Madjid Gordji, Dong Shin   +6 more
core   +1 more source

Asymptotic behavior of Fréchet functional equation and some characterizations of inner product spaces

Demonstratio Mathematica, 2023
This article presents the general solution f:G→Vf:{\mathcal{G}}\to {\mathcal{V}} of the following functional equation: f(x)−4f(x+y)+6f(x+2y)−4f(x+3y)+f(x+4y)=0,x,y∈G,f\left(x)-4f\left(x+y)+6f\left(x+2y)-4f\left(x+3y)+f\left(x+4y)=0,\hspace{1.0em}x,y\in {\
Park Choonkil, Tareeghee Mohammad Amin, Najati Abbas, Yengejeh Yavar Khedmati, Paokanta Siriluk   +4 more
doaj   +1 more source

The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

Demonstratio Mathematica, 2020
In this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x−3y)+f(x+2y)+f(x−2y)+22f(x)+24f(y)=13[f(x+y)+f(x−y)]+12f(2y),f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]
Thanyacharoen Anurak, Sintunavarat Wutiphol   +1 more
doaj   +1 more source