EuDML | Browse

We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological equation φ(Fx)...

The addition formula for theta functions.

Mario Bonk (1997)

Aequationes mathematicae

The addition theorem of Weierstrass' s sigma function.

Mario Bonk (1994)

Mathematische Annalen

The additive approximation on a four-variate Jensen-type operator equation.

Wang, Jian (2003)

International Journal of Mathematics and Mathematical Sciences

The associativity equation revisited.

R. Craigen, Z. Páles (1989)

Aequationes mathematicae

The Beckman-Quarles theorem for mappings from $ℂ^{2}$ to $ℂ^{2}$ .

Tyszka, Apoloniusz (2005)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

The Binet-Pexider functional equation for rectangular matrices.

K.J. Heuvers, D.S. Moak (1990)

Aequationes mathematicae

The $C^{1}$ solutions of the series-like iterative equation with variable coefficients.

Mi, Yuzhen, Li, Xiaopei, Ma, Ling (2009)

Fixed Point Theory and Applications [electronic only]

The cardinality of the set of discontinuous solutions of a class of functional equations.

Walter Benz (1987)

Aequationes mathematicae

The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation

Janusz Brzdęk (1996)

Annales Polonici Mathematici

Let K denote the set of all reals or complex numbers. Let X be a topological linear separable F-space over K. The following generalization of the result of C. G. Popa [16] is proved. Theorem. Let n be a positive integer. If a Christensen measurable function f: X → K satisfies the functional equation $f (x + f {(x)}^{n} y) = f (x) f (y)$ , then it is continuous or the set x ∈ X : f(x) ≠ 0 is a Christensen zero set.

The cocycle equation in division rings.

J. Lawrence (1981)

Aequationes mathematicae

The complete polynomial grid

R. V. Parker (1973)

Matematički Vesnik

The Complete Solution of Hosszú's Functional Equation Over a Field. (Short Communication).

T.M.K. Davison (1974)

Aequationes mathematicae

The Complete Solution of Hosszú's Functional Equation Over a Field.

T.M.K. Davison (1974)

Aequationes mathematicae

The continuous solution of a functional equation of Abel.

Maciej Sablik (1990)

Aequationes mathematicae

The continuous solutions of a generalized Dhombres functional equation

L. Reich, Jaroslav Smítal, M. Štefánková (2004)

Mathematica Bohemica

We consider the functional equation $f (x f (x)) = ϕ (f (x))$ where $ϕ J \to J$ is a given increasing homeomorphism of an open interval $J \subset (0, \infty)$ and $f (0, \infty) \to J$ is an unknown continuous function. In a series of papers by P. Kahlig and J. Smítal it was proved that the range of any non-constant solution is an interval whose end-points are fixed under $ϕ$ and which contains in its interior no fixed point except for $1$ . They also provide a characterization of the class of monotone solutions and prove a necessary and sufficient condition for any solution...

The convergence of an implicit mean value iteration.

Rhoades, B.E., Şoltuz, Ştefan M. (2006)

International Journal of Mathematics and Mathematical Sciences

Currently displaying 1 – 20 of 137

Page 1 Next