Results 241 to 250 of about 1,745 (271)

Jensen and Quadratic Functional Equations on Semigroups

2012
Let S be a commutative semigroup, σ:S→S an endomorphism of order 2, G a 2-cancellative abelian group, and n a positive integer. One of the goals of this paper is to determine the general solutions of the functional equations f 1(x+y)+f 2(x+σy)=f 3(x) and also f 1(x+y)+f 2(x+σy)=f 3(x)+f 4(y) for all x,y∈S n , where f 1,f 2,f 3,f 4:S n →G are unknown ...
Esteban A. Chávez, Prasanna K. Sahoo
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Alternative Jensen type functional equation

Let X and Y be linear spaces over a field F where F = Q,R or C and let f : X-> Y be arbitrary function. Given a constant p R such that p # 0,1, we prove that the alternative Jensen type functional equation pf(x)+(1-p) f (y) = -+f(px+ (1-p)y) is equivalent to the Jensen type functional equation pf(x)+(1-p) f (y) = -+f(px+ (1-p)y) Moreover, we prove ...
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Alienation and stability of Jensen’s and other functional equations

Aequationes mathematicae
\textit{J. Dhombres} [Aequationes Math. 35, No. 2--3, 186--212 (1988; Zbl 0654.39003)] introduced the notion of alienation of functional equations: consider the functional equation \(E(f,g)=0\) obtained by summing up two functional equations \(E_1(f)=0\) and \(E_2(g)=0\) side by side. If the equation \(E(f,g)=E_1(f)+E_2(g)=0\) splits back to the system
Tial, Mohamed, Zeglami, Driss
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Hyperstability of an n-dimensional Jensen type functional equation

Afrika Matematika, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Solution of Generalized Jensen and Quadratic Functional Equations

2019
We obtain in terms of additive and multi-additive functions the general solution f : S → H of each of the functional equations $$\displaystyle \sum _{\lambda \in \varPhi } f(x+\lambda y+a_{\lambda })=Nf(x),\ x,y\in S, $$ $$\displaystyle \sum _{\lambda \in \varPhi }f(x+\lambda y+a_{\lambda })=Nf(x)+Nf(y),\ x,y\in S, $$ where (S, +) is an ...
A. Charifi, D. Zeglami, S. Kabbaj
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Alternative jensen functional equation on groups

Given integers α, β, γ such that (α, β, γ) ̸= k(1,−2, 1) for all k ∈ Z, we will establish a criterion for the existence of the general solution of the alternative Jensen functional equation of the form f(xy^{−1}) − 2f(x) + f(xy) = 0 or αf(xy^{−1}) + βf(x) + γf(xy) = 0, where f is a mapping from a group (G, ·) to a uniquely divisible abelian group (H, +)
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Non-Archimedean stability of Cauchy-Jensen type functional equation

2011
Summary: In this paper we investigate the generalized Hyers-Ulam stability of the following Cauchy-Jensen-type functional equation \[ Q\left(\frac{x+y}{2}+z\right)+Q\left(\frac{x+z}{2}+y\right)+Q\left(\frac{z+y}{2}+x\right)=2[Q(x)+Q(y)+Q(z)] \] in non-Archimedean spaces.
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Jensen's functional equation

2002
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Functional nanoparticles through π-conjugated polymer self-assembly

Nature Reviews Materials, 2020
Liam R Macfarlane, Huda Shaikh, Juan Diego Garcia-Hernandez   +2 more
exaly  

Metal Ion-Directed Functional Metal–Phenolic Materials

Chemical Reviews, 2022
Huimin Geng, Qi-Zhi Zhong, Jianhua Li
exaly