Results 231 to 240 of about 1,745 (271)

Jensen’s functional equation on semigroups

Acta Mathematica Hungarica, 2023
The author considers the functional equation \[f(x\varphi(y))+f(\psi(y)x)=2f(x), \quad x,y\in S,\tag{1}\] with \(s\colon S\to H\), \(S\) a semigroup, \(H\) a 2-torsion free abelian group and \(\varphi,\psi\colon S\to S\) endomorphisms.\par It is shown that under the assumption that \(\varphi\) or \(\psi\) is surjective the solutions of (1) are of the ...
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Jensen's functional equation on groups, III

Aequationes Mathematicae, 1999
[For part I see ibid. 39, No.1, 85-99 (1990; Zbl 0688.39007); see also \textit{J. C. Parnami} and \textit{H. L. Vasudeva}, ibid. 43, No. 2/3, 211-218 (1992; Zbl 0755.39008).] Let \((G,\cdot)\) be a group and \((H,+)\) an abelian group, and \(f:G\to H\) a mapping. Let \(e\) denote the identity of \(G\) and \(0\) that of \(H\).
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On Jensen’s functional equation on groups

Aequationes mathematicae, 2003
The classical Jensen's functional equation is known as [see \textit{J. Aczél}, Lectures on functional equatons and their applications (Academic Press, London) (1966; Zbl 0139.09301)] \[ f\Biggl({x+y\over 2}\Biggr)= {f(x)+ f(y)\over 2} \] which with \(x= u+v\), \(y= u-v\) becomes \(f(u+ v)+ f(u- v)= 2f(u)\), transparent for generalization for a group ...
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Hyperstability of the Jensen functional equation

Acta Mathematica Hungarica, 2013
\textit{S.-M. Jung}, \textit{M. S. Moslehian} and \textit{P. K. Sahoo} [J. Math. Inequal. 4, No. 2, 191--206 (2010; Zbl 1219.39016)] investigated the conditional stability of the generalized Jensen functional equation \(f(ax+by)=af(x)+bf(y)\). Based on a fixed point method, the authors of the present paper consider the hyperstability problem of the ...
Bahyrycz, A., Piszczek, M.
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A Pexider–Jensen functional equation on groups

Aequationes mathematicae, 2005
Let \((G,\cdot)\) be a group, \((H,+)\) an abelian group, and \(f,g,h:G\to H.\) The Pexider-Jensen functional equation \[ f(x.y)+g(x.y^{-1})=h(x) \] is studied. The author obtains the solution of this equation on free groups and outlines a process to find the solution on other groups. Some results on Jensen's equation are extended. The results obtained
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Fuzzy stability of the Jensen functional equation

Fuzzy Sets and Systems, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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