Results 261 to 270 of about 1,517,675 (283)

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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Lipschitz Stability of the Cauchy and Jensen Equations

Results in Mathematics, 1997
Let \(G\) be a semigroup and let \(E\) be a normed space. Let \(\mathcal F\) be a given set of functions from \(G\) into \(E\), and let \(\widetilde{\mathcal F}\) be a given set of functions from \(G\times G\) into \(E\). The pair \(({\mathcal F},\widetilde{\mathcal F})\) has the double difference property if for every \(f:G\to E\) such that ...
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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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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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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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Jensen’s Inequality for Backward Stochastic Differential Equations*

Chinese Annals of Mathematics, Series B, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Generalization of the Hyers–Ulam–Rassias Stability of Jensen's Equation

Journal of Mathematical Analysis and Applications, 1999
Yang-Hi Lee, Kil-Woung Jun
exaly  

On a Cauchy–Jensen functional equation and its stability

Journal of Mathematical Analysis and Applications, 2006
Won-Gil Park
exaly  

ON THE SOLUTIONS OF A BI-JENSEN FUNCTIONAL EQUATION AND ITS STABILITY

Bulletin of the Korean Mathematical Society, 2006
Jae Hyeong Bae, Won-Gil Park
exaly  

Jensen's functional equation

2002
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