Results 251 to 260 of about 153,653 (286)

Fuzzy stability of the Jensen functional equation

Fuzzy Sets and Systems, 2008
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Mirmostafaee, A. K., Mirzavaziri, M., Moslehian, M. S.   +2 more
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Jensen’s Functional Equation

2011
There are a number of variations of the additive Cauchy functional equation, for example, generalized additive Cauchy equations appearing in Chapter 3, Hosszu’s equation, homogeneous equation, linear functional equation, etc. However, Jensen’s functional equation is the simplest and the most important one among them.
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On a Mikusiński—Jensen Functional Equation

2002
The following Mikusinski-Jensen type functional equation is investigated. The main result states that if I is an open real interval, or more generally, if I is a convex subset of a linear space whose intersection with straight lines is an open segment, then the above equation is equivalent to the so called Jensen functional equation.
Károly Lajkó, Zsolt Páles
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On Jensen-like form of Mikusiński's functional equation

Acta Mathematica Hungarica
The paper investigates the following conditional version of Mikusiński's functional equation \[f(x+y)\neq 0 \quad \Rightarrow \quad 2f\left(\frac{x+y}{2}\right)= f(x)+f(y), \] for functions between uniquely 2-divisible groups, with the codomain being abelian.
Imani, E., Najati, A., Tareeghee, M. A.
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Note on a Jensen type functional equation

Publicationes Mathematicae Debrecen, 2003
The author examines the stability of the functional equation \( f: M \to S\) \[ 3f \left( \frac{x+y+z}{3} \right) + f(x) + f(y) + f(z)=2\left[ f\left ( \frac{x+y}{2} \right) + f\left(\frac{y+z}{2} \right) + f \left ( \frac{z+x}{2} \right) \right], \] where \(M\) is an abelian semigroup in which the division by \(2\) and \(3\) is performable and \(S ...
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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
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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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