Results 81 to 90 of about 4,528,914 (107)
Set-Valued Solutions of the Pexider Functional Equation
Set-Valued Solutions of the Pexider Functional Equationopenaire +1 more source
A Third Logarithmic Functional Equation and Pexider Generalizations
Aequationes Mathematicae, 2005 If \( f: ] 0, \infty [ \to R\) is a real valued function defined on the set of positive reals one may consider the three functional equations: (1) \( f(x+y) - f(xy) = f(1/x + 1/y)\), (2) \( f(x + y) - f(x) - f(y) = f(1/x, + 1/y )\), (3) \( f(xy ) = f(x) + f(y)\). The authors show that the three equations are equivalent.
Konrad J Heuvers
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On Pexider Additive Functional Equations
Multidiszciplináris Tudományok, 2023 Let Y(+) egy Abelian group, D in Z2 ( Z(+,≤) denotes the ordered group of the integers).Dx:={uϵZ | exists vϵ X; (u,v)ϵ D}, Dy:={vϵZ | exists uϵ X; (u,v)ϵ D}, Dx+y:={zϵZ | exists (u,v)ϵ D; z=u+v}.The aim of the article is to find sets D in Z2 that the general solution of the functional equation f(x+y) = g(x) + h(y) ((x,y ϵ D) with unknown functions f, g
Glavosits Tamás
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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
Che Tat Ng
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A New Functional Equation Analogous to CAUCHT-PEXIDER Functional Equation and Its Application
Biometrical Journal, 1978AbstractThe CAUCHY‐PEXIDER functional equationH(x±y)=F(x)G(y) is generalized to the formH((xc±yc)1/c) =F(x)G(y),c≠0, assuming the functionH(x) possesses a measurable majorant on a set of positive measure. The result is used to obtain a characterization of WEIBULL distribution. This functional equation is generalized to functions of vector variables.
K G Janardan
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The Pexider Functional Equations in Distributions
Canadian Journal of Mathematics, 1990The Cauchy functional equations have been studied recently for Schwartz distributions by Koh in [3]. When the solutions are locally integrate functions, the equations reduce to the classical Cauchy equations (see [1]):(1) f(x+y)=f﹛x)+f(y)(2) f(x+y)=f(x)f(y)(3) f(xy)=f(x)+f(y)(4) f(xy)=f(x)f(y).Earlier efforts to study functional equations in ...
E. Y. Deeba, E. L. Koh
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A New Functional Equation of Pexider Type Related to the Complex Exponential Function [PDF]
Transactions of the American Mathematical Society, 1995 The purpose of this paper is to solve a new functional equation, characteristic for the complex exponential function, which contains four unknown entire functions and to solve, as an application, three further functional equations.
Hiroshi Haruki, Themistocles M Rassias
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A functional equation of Pexider type
Funkcialaj Ekvacioj, 1992All entire solutions \(f\), \(g\), \(h\), \(k\) of the functional equation \(| f(z+w)|+| g(z-w)|=| h(z+\bar w)+| k(z-\bar w)|\) are determined. They are all of the form \(\varphi^ 2\), where \(\varphi\) is either a linear function or a linear combination of two exponential functions. The proof is based on the observation that each of the functions \(f\)
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On the Superstability of the Pexider Type Generalized Trigonometric Functional Equations
Acta Mathematica Scientia, 2014Abstract The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation ∑ ϕ ∈ Φ ∫ K f ( x k ϕ ( y ) k - 1 ) d u K ( k ) = | Φ | g ( x ) h ( y ) , x , y ∈ G , where G is any topological group, K is ...
Samir Kabbaj +2 more
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On a pexider-type functional equation for quasideviation means
Acta Mathematica Hungarica, 1988The equation \[ K_{mn}(x_ 1y_ 1,...,x_ my_ 1,...,x_ 1y_ n,...,x_ my_ n)=M_ m(x_ 1,...,x_ m)N_ n(y_ 1,...,y_ n)\quad (x_ 1,...,x_ m,y_ 1,...,y_ n>0) \] is solved for quasideviation means [see the author's definition in Acta Math. Acad. Sci. Hungar. 40, 243-260 (1982; Zbl 0541.26006)]. The solutions correspond to those found by \textit{Z.
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