The converse problem for a generalized Dhombres functional equation

L. Reich; Jaroslav Smítal; M. Štefánková

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Displaying similar documents to “The converse problem for a generalized Dhombres functional equation”

On a generalized Dhombres functional equation. II.

P. Kahlig, Jaroslav Smítal (2002)

Mathematica Bohemica

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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 previous paper we proved that no continuous solution can cross the line $y = p$ where $p$ is a fixed point of $ϕ$ , with a possible exception for $p = 1$ . The range of any non-constant continuous solution is an interval whose end-points are fixed by $ϕ$ and which contains in its interior no fixed point except for $1$ . We also gave a characterization of the...

Monotone extenders for bounded c-valued functions

Kaori Yamazaki (2010)

Studia Mathematica

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Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, $C_{\infty} (A, c)$ the set of all bounded continuous functions f: A → c, and $C_{A} (X, c)$ the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender $u : C_{\infty} (A, c) \to C_{A} (X, c)$ . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer...

Solutions for the p-order Feigenbaum’s functional equation $h (g (x)) = g^{p} (h (x))$

Min Zhang, Jianguo Si (2014)

Annales Polonici Mathematici

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This work deals with Feigenbaum’s functional equation ⎧ $h (g (x)) = g^{p} (h (x))$ , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, $g^{p}$ is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.

Second order quasilinear functional evolution equations

László Simon (2015)

Mathematica Bohemica

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We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in $(0, T)$ is proved and examples satisfying the assumptions of the existence theorem are formulated. Then a uniqueness theorem is proved. Finally, existence and some qualitative properties of the solutions in $(0, \infty)$ (boundedness and stabilization as $t \to \infty$ ) are shown.

On the Rockafellar theorem for $Φ^{γ (\cdot, \cdot)}$ -monotone multifunctions

S. Rolewicz (2006)

Studia Mathematica

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Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let $Γ : X \to 2^{Φ}$ be a cyclic $Φ^{γ (\cdot, \cdot)}$ -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the $Φ^{γ (\cdot, \cdot)}$ -subdifferential of f, $Γ (x) \subset \partial_{Φ}^{γ (\cdot, \cdot)} {f |}_{x}$ .

The law of large numbers and a functional equation

Maciej Sablik (1998)

Annales Polonici Mathematici

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We deal with the linear functional equation (E) $g (x) = \sum_{i = 1}^{r} p_{i} g (c_{i} x)$ , where g:(0,∞) → (0,∞) is unknown, $(p ₁, . . ., p_{r})$ is a probability distribution, and $c_{i}$ ’s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli’s Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.

Function spaces and local properties

Ziqin Feng, Paul Gartside (2013)

Fundamenta Mathematicae

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Necessary conditions and sufficient conditions are given for $C_{p} (X)$ to be a (σ-) m₁- or m₃-space. (A space is an m₁-space if each of its points has a closure-preserving local base.) A compact uncountable space K is given with $C_{p} (K)$ an m₁-space, which answers questions raised by Dow, Ramírez Martínez and Tkachuk (2010) and Tkachuk (2011).

Displaying similar documents to “The converse problem for a generalized Dhombres functional equation”

On a generalized Dhombres functional equation. II.

Monotone extenders for bounded c-valued functions

Solutions for the p-order Feigenbaum’s functional equation h ( g ( x ) ) = g p ( h ( x ) )

Second order quasilinear functional evolution equations

On the Rockafellar theorem for Φ γ ( · , · ) -monotone multifunctions

The law of large numbers and a functional equation

Function spaces and local properties

Solutions for the p-order Feigenbaum’s functional equation $h (g (x)) = g^{p} (h (x))$

On the Rockafellar theorem for $Φ^{γ (\cdot, \cdot)}$ -monotone multifunctions