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

Min Zhang; Jianguo Si

Displaying similar documents to “Solutions for the p-order Feigenbaum’s functional equation $h (g (x)) = g^{p} (h (x))$ ”

On the functional equation $f (x) + \sum_{i = 1}^{n} g_{i} (y_{i}) = h (T (x, y_{1}, y_{2}, . . ., y_{n}))$

C. T. Ng (1973)

Annales Polonici Mathematici

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$C^{r}$ -solutions of a system of functional equations

Z. Kominek (1974)

Annales Polonici Mathematici

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On some symmetrical equations of the form $f_{1} (x_{1} + . . . + x_{n}) = \sum_{i_{1}, . . ., i_{n}}) f_{1} (x_{i} 1) . . . f_{n} (x_{i} n)$

H. Światak (1967)

Annales Polonici Mathematici

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On the solutions of the functional equation $ϕ (x) + ϕ^{2} (x) = F (x)$

M. Malenica (1982)

Matematički Vesnik

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On the Functional Equation $f (λ) + f (ω λ) f (ω^{- 1} λ) = 1$ , $(ω^{5} = 1)$

Yasutaka Sibuya (1984)

Recherche Coopérative sur Programme n°25

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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 Probability Distribution Solutions of a Functional Equation

Janusz Morawiec, Ludwig Reich (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let 0 < β < α < 1 and let p ∈ (0,1). We consider the functional equation φ(x) = pφ (x-β)/(1-β) + (1-p)φ(minx/α, (x(α-β)+β(1-α))/α(1-β)) and its solutions in two classes of functions, namely ℐ = φ: ℝ → ℝ|φ is increasing, ${φ |}_{(- \infty, 0]} = 0$ , ${φ |}_{[1, \infty)} = 1$ , = φ: ℝ → ℝ|φ is continuous, ${φ |}_{(- \infty, 0]} = 0$ , ${φ |}_{[1, \infty)} = 1$ . We prove that the above equation has at most one solution in and that for some parameters α,β and p such a solution exists, and for some it does not. We also determine all solutions of the equation in ℐ and we show the...

A useful algebra for functional calculus

Mohammed Hemdaoui (2019)

Mathematica Bohemica

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We show that some unital complex commutative LF-algebra of $𝒞^{(\infty)}$ $ℕ$ -tempered functions on $ℝ^{+}$ (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.

On the Schröder equation

M. Kuczma

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CONTENTSPART IIntroduction............................................................................................... 31. General solution.................................................................................. 42. Preliminaries and notation................................................................ 53. $C^{p}$ solutions in $ℭ$ *................................................ 74. Change of variables..............................................................................

The functional equation $f^{2} (x) = g (x)$

James C. Lillo (1967)

Annales Polonici Mathematici

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A note on functional tightness and minitightness of space of the $G$ -permutation degree

Dimitrios N. Georgiou, Nodirbek K. Mamadaliev, Rustam M. Zhuraev (2023)

Commentationes Mathematicae Universitatis Carolinae

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We study the behavior of the minimal tightness and functional tightness of topological spaces under the influence of the functor of the permutation degree. Analytically: a) We introduce the notion of $τ$ -open sets and investigate some basic properties of them. b) We prove that if the map $f : X \to Y$ is $τ$ -continuous, then the map $S P^{n} f : S P^{n} X \to S P^{n} Y$ is also $τ$ -continuous. c) We show that the functor $S P^{n}$ preserves the functional tightness and the minimal tightness of compacts. d) Finally, we give some facts and properties...

A bifurcation theory for some nonlinear elliptic equations

Biagio Ricceri (2003)

Colloquium Mathematicae

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We deal with the problem ⎧ -Δu = f(x,u) + λg(x,u), in Ω, ⎨ ( $P_{λ}$ ) ⎩ $u_{∣ \partial Ω} = 0$ where Ω ⊂ ℝⁿ is a bounded domain, λ ∈ ℝ, and f,g: Ω×ℝ → ℝ are two Carathéodory functions with f(x,0) = g(x,0) = 0. Under suitable assumptions, we prove that there exists λ* > 0 such that, for each λ ∈ (0,λ*), problem ( $P_{λ}$ ) admits a non-zero, non-negative strong solution $u_{λ} \in ⋂_{p \geq 2} W^{2, p} (Ω)$ such that $l i m_{λ \to 0 ⁺} | | u_{λ} {| |}_{W^{2, p} (Ω)} = 0$ for all p ≥ 2. Moreover, the function $λ \mapsto I_{λ} (u_{λ})$ is negative and decreasing in ]0,λ*[, where $I_{λ}$ is the energy functional related to ( $P_{λ}$ ). ...

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

On square functions associated to sectorial operators

Christian Le Merdy (2004)

Bulletin de la Société Mathématique de France

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We give new results on square functions ${∥ x ∥}_{F} = ∥ {(\int_{0}^{\infty} {|F (t A) x|}^{2} \frac{d t}{t})}^{1 / 2} ∥_{p}$ associated to a sectorial operator $A$ on $L^{p}$ for $1 < p < \infty$ . Under the assumption that $A$ is actually $R$ -sectorial, we prove equivalences of the form $K^{- 1} {∥ x ∥}_{G} \leq {∥ x ∥}_{F} \leq K {∥ x ∥}_{G}$ for suitable functions $F, G$ . We also show that $A$ has a bounded $H^{\infty}$ functional calculus with respect to ${∥ . ∥}_{F}$ . Then we apply our results to the study of conditions under which we have an estimate $∥ {(\int_{0}^{\infty} | C e^{- t A} {(x) |}^{2} d t)^{1 / 2} ∥}_{q} \leq M {∥ x ∥}_{p}$ , when $- A$ generates a bounded semigroup $e^{- t A}$ on $L^{p}$ and $C : D (A) \to L^{q}$ is a linear mapping.

Displaying similar documents to “Solutions for the p-order Feigenbaum’s functional equation h ( g ( x ) ) = g p ( h ( x ) ) ”

Displaying similar documents to “Solutions for the p-order Feigenbaum’s functional equation $h (g (x)) = g^{p} (h (x))$ ”