Results 211 to 220 of about 152,222 (241)

Multi-scale effects of habitat loss and the role of trait evolution. [PDF]

Ecol Evol
Bagawade R, van Benthem KJ, Wittmann MJ.
europepmc   +1 more source

Jensen's functional equation [PDF]

, 2002
S. Czerwik
semanticscholar   +6 more sources

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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 ...
A. Akkaoui
semanticscholar   +2 more sources

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 ...
H. Stetkær
semanticscholar   +3 more sources

Jensen's functional equation on groups, II

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 \(H\).
C. T. Ng
semanticscholar   +4 more sources

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.
Soon-Mo Jung
semanticscholar   +2 more sources

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
C. T. Ng
semanticscholar   +3 more sources

A proof of the equivalence of the equation*(x+y−xy)+*(xy)=*(x)+*(y) and Jensen's functional equation [PDF]

, 1971
H. Światak
semanticscholar   +2 more sources

Jensen’s Functional Equation

, 2013
H. Stetkær
semanticscholar   +2 more sources