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A Pexider–Jensen functional equation on groups
Aequationes Mathematicae, 2005Let \((G,\cdot)\) 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
Ng Che Tat, Che Tat Ng
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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 ...
Magdalena Piszczek +2 more
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Hyers–Ulam–Rassias Stability of a Jensen Type Functional Equation [PDF]
In this paper we solve the Jensen type functional equation (1.1).
Tiberiu Trif
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Stability of Cauchy–Jensen type functional equation in generalized fuzzy normed spaces [PDF]
In this paper, we establish some stability results concerning the Cauchy–Jensen functional equation in generalized fuzzy normed spaces.
Hamid Khodaei, M Eshaghi Gordji
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Intuitionistic fuzzy stability of a Jensen functional equation via fixed point technique [PDF]
The object of this paper is to determine Hyers-Ulam-Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation
Murat Cancan, S A Mohiuddine
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Jensen’s functional equation on semigroups
Acta Mathematica Hungarica, 2023The 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, 2003The 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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