Results 251 to 260 of about 1,517,675 (283)

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 ...
Magdalena Piszczek, Anna Bahyrycz
exaly   +2 more sources

Hyers–Ulam–Rassias Stability of a Jensen Type Functional Equation [PDF]

Journal of Mathematical Analysis and Applications, 2000
In this paper we solve the Jensen type functional equation (1.1).
Tiberiu Trif
exaly   +2 more sources

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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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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Fuzzy stability of the Jensen functional equation

Fuzzy Sets and Systems, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alireza Kamel Mirmostafaee, Madjid Mirzavaziri, Mohammad Sal Moslehian   +2 more
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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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Jensen's equation and bisymmetry

Publicationes Mathematicae Debrecen, 2002
The theorem of this note characterizes those \(n\)-bisymmetric functions that are continuous and strictly increasing in each variable, in terms of \(n\)-weights. The characterization is known, but the author presents a short and simple proof of it. The proof is based on the result in the special case of \(n=2\), which is due to \textit{J.
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On stability for the Jensen equation on intervals

Aequationes Mathematicae, 2000
The paper discusses the stability properties of the Jensen equation \[ f\left (\frac{x+y}{2}\right)=\frac{f(x)+f(y)}{2}, \qquad x,y\in D \tag{1} \] for real valued functions. These functions are assumed to be defined on the domain \(D=I\cap (G+\gamma)\), where \(G\) is a \(2\)-divisible subgroup of \(\mathbb R\), \(I\subset\mathbb R\) is an interval ...
Boros, Zoltan, Pales, Zsolt, Volkmann, Peter   +2 more
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Superstability of the Cauchy, Jensen and Isometry Equations

Results in Mathematics, 1999
The author generalizes the results of \textit{J. Tabor} [Result Math. 32, No. 1-2, 145-158 (1997; Zbl 0890.39024)] for the superstability of the Cauchy and Jensen functional equation almost everywhere. A theorem is also proved concerning the superstability of the isometry equation in inner product spaces.
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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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