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 → J is a given increasing homeomorphism of an open interval J ⊂ ( 0 , ∞ ) and f ( 0 , ∞ ) → 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 ∞ ( 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 ∞ ( A , c ) → 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 , ∞ ) (boundedness and stabilization as t → ∞ ) are shown.

On the Rockafellar theorem for Φ γ ( · , · ) -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 → 2 Φ be a cyclic Φ γ ( · , · ) -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 ( · , · ) -subdifferential of f, Γ ( x ) ⊂ ∂ Φ γ ( · , · ) 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 ) = ∑ 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).