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On a Jensen Type Functional Equation [PDF]
Journal of Applied Analysis, 2007 Suppose that \(M\) is a Abelian group in which the unique division by 2 and 3 is performable and \(S\) is an abstract cone satisfying the cancellation law. In this paper the author proves that if \(f:M\to S\) is a solution of the Jensen functional equation, then it is a solution of the following equation \[ 3(b-1) f\biggl(\frac{x+y+z}{3}\biggr)+ f(x)+f(
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On Jensen's functional equation
Aequationes Mathematicae, 1992 The following is offered as main result. Let \((G,\cdot)\) and \((H,+)\) be abelian groups, and \(e\) the neutral element of \((G,\cdot)\). The solutions \(f: G\to H\) of \(f(xy)+f(xy^{-1})=2f(x)\), \(f(e)=0\) are exactly the homomorphisms of \(G\to H\) if, and only if, either \(H\) has no element of order 2 or \([G:G^ 2]\leq 2\), where \(G^ 2:=\{x^ 2 ...
Vasudeva, H.L., Parnami, J.C.
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Generalized Jensen functional equation on restricted domain
Annals of the West University of Timisoara: Mathematics and Computer Science, 2014 We prove the Hyers-Ulam stability on restricted domains of generalized Jensen functional ...
Chahbi Abdellatif +3 more
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On Jensen’s and the quadratic functional equations with involutions [PDF]
Proyecciones (Antofagasta), 2017 We determine the Solutions f : S → H of the generalized Jensen’s functional equation f( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y∈ Sand the solutions f : S → H of the generalized quadratic functional equationf ( x + σ(y)) + f (x + τ(y)) = 2f (x) + 2f (y), x, y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Fadli, B. +3 more
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Jensen’s and the quadratic functional equations with an endomorphism [PDF]
Proyecciones (Antofagasta), 2017 We determine the solutions f : S → H of the generalized Jensen’s functional equation f (x + y) + f (x + φ(y)) = 2f (x), x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equation f (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first ...
Sabour, KH, Kabbaj, S
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Jensen-Shannon distance between men and women.
, 2022 Jensen-Shannon distance between men and women.
Lanu Kim (11262926) +8 more
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ON CONDITIONAL JENSEN EQUATION
Demonstratio Mathematica, 2001 The author extends some results of \textit{C. Alsina} and \textit{J. L. Garcia-Roig} [in `Functional analysis, approximation theory and numerical analysis', Singapore: World Scientific, 5-7 (1994; Zbl 0877.39015)], \textit{R. Ger} and \textit{J. Sikorska} [Pr. Nauk. Univ. Śląsk. Katowicach, Ann. Math. Silesianae 1665, No.
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Functional Differential Equations and Jensen’s Inequality [PDF]
Journal of Mathematical Analysis and Applications, 1987 The authors study various types of stability of the functional differential equations \(x'(t)=F(t,x_ t)\) where \(x_ t(s)=x(t+s),\)- h\(\leq s\leq 0\), and h is a positive constant. The main tool is the Lyapunov functionals. These functionals satisfy certain conditions involving functions which verify Jensen's inequality.
Becker, Leigh C +2 more
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On a Jensen-Hosszú equation, II [PDF]
Mathematical Inequalities & Applications, 2012 We solve functional equation of the form f (x+ y− xy)+ f (xy) = 2 f ( x+ y 2 ) in the class of functions transforming the unit interval into the space of all reals. We also prove that this equation is stable in the Hyers-Ulam’s sense. Mathematics subject classification (2010): 39B82, 39B62, 26A61.
Zygfryd Kominek, Justyna Sikorska
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ch-jensen/participants: Semantic mapping of participants
, 2019 <p><a href="https://github.com/ch-jensen/participants/files/2813282/actor-tf-c.zip">actor-tf-c.zip</a></p ...
Christian Højgaard Jensen
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