## Displaying similar documents to “On functional differential inclusions in Hilbert spaces”

### Continuous solutions of the functional equation $\phi \left(f\left(x\right)\right)=G\left(x,\phi \left(x\right)\right)$ for vector-valued functions φ

Annales Polonici Mathematici

Similarity:

### Method of averaging for the system of functional-differential inclusions

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧$ẋ\left(t\right)\in F\left(t,{x}_{t},{y}_{t}\right)$ (0) ⎨ ⎩$ẋ\left(t\right)\in G\left(t,{x}_{t},{y}_{t}\right)$ (1)

### The functional equation ${f}^{2}\left(x\right)=g\left(x\right)$

Annales Polonici Mathematici

Similarity:

### Second order quasilinear functional evolution equations

Mathematica Bohemica

Similarity:

We consider second order quasilinear evolution equations where also the main part contains functional dependence on the unknown function. First, existence of solutions in $\left(0,T\right)$ 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 $\left(0,\infty \right)$ (boundedness and stabilization as $t\to \infty$) are shown.

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

Annales Polonici Mathematici

Similarity:

This work deals with Feigenbaum’s functional equation ⎧ $h\left(g\left(x\right)\right)={g}^{p}\left(h\left(x\right)\right)$, ⎨ ⎩ 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.

### On the functional equation $f\left(x+y-xy\right)+f\left(xy\right)=f\left(x\right)+f\left(y\right)$

Matematički Vesnik

Similarity:

### Equivalence of multi-norms

Similarity:

The theory of multi-norms was developed by H. G. Dales and M. E. Polyakov in a memoir that was published in Dissertationes Mathematicae. In that memoir, the notion of ’equivalence’ of multi-norms was defined. In the present memoir, we make a systematic study of when various pairs of multi-norms are mutually equivalent. In particular, we study when (p,q)-multi-norms defined on spaces ${L}^{r}\left(\Omega \right)$ are equivalent, resolving most cases; we have stronger results in the case where r = 2. We also show...

### ${H}^{\infty }$ functional calculus for sectorial and bisectorial operators

Studia Mathematica

Similarity:

We give a concise exposition of the basic theory of ${H}^{\infty }$ functional calculus for N-tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator $f\left(T₁,...,{T}_{N}\right)$ when f is an R-bounded operator-valued holomorphic function.

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

Annales Polonici Mathematici

Similarity:

### On the functional equation $f\left(x\right)+{\sum }_{i=1}^{n}{g}_{i}\left({y}_{i}\right)=h\left(T\left(x,{y}_{1},{y}_{2},...,{y}_{n}\right)\right)$

Annales Polonici Mathematici

Similarity:

### On the solutions of the functional equation $\varphi \left(x\right)+{\varphi }^{2}\left(x\right)=F\left(x\right)$

Matematički Vesnik

Similarity:

### On some symmetrical equations of the form ${f}_{1}\left({x}_{1}+...+{x}_{n}\right)={\sum }_{{i}_{1},...,{i}_{n}}\right){f}_{1}\left({x}_{i}1\right)...{f}_{n}\left({x}_{i}n\right)$

Annales Polonici Mathematici

Similarity:

### The law of large numbers and a functional equation

Annales Polonici Mathematici

Similarity:

We deal with the linear functional equation (E) $g\left(x\right)={\sum }_{i=1}^{r}{p}_{i}g\left({c}_{i}x\right)$, where g:(0,∞) → (0,∞) is unknown, $\left(p₁,...,{p}_{r}\right)$ 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.

### A pair of linear functional inequalities and a characterization of ${L}^{p}$-norm

Annales Polonici Mathematici

Similarity:

It is shown that, under some general algebraic conditions on fixed real numbers a,b,α,β, every solution f:ℝ → ℝ of the system of functional inequalities f(x+a) ≤ f(x)+α, f(x+b) ≤ f(x)+β that is continuous at some point must be a linear function (up to an additive constant). Analogous results for three other similar simultaneous systems are presented. An application to a characterization of ${L}^{p}$-norm is given.

### $\alpha$-continuous multivalued maps

Matematički Vesnik

Similarity:

### On the separation properties of ${K}_{\omega }$

Colloquium Mathematicae

Similarity:

### CM-Selectors for pairs of oppositely semicontinuous multivalued maps with ${}_{p}$-decomposable values

Studia Mathematica

Similarity:

We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex ${L}_{p}\left(T,E\right)$-decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, ${L}_{p}\left(T,E\right)$ is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x)...

### Monotone extenders for bounded c-valued functions

Studia Mathematica

Similarity:

Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, ${C}_{\infty }\left(A,c\right)$ the set of all bounded continuous functions f: A → c, and ${C}_{A}\left(X,c\right)$ 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 $u:{C}_{\infty }\left(A,c\right)\to {C}_{A}\left(X,c\right)$. This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer...

### Selection principles and upper semicontinuous functions

Colloquium Mathematicae

Similarity:

In connection with a conjecture of Scheepers, Bukovský introduced properties wQN* and SSP* and asked whether wQN* implies SSP*. We prove it in this paper. We also give characterizations of properties S₁(Γ,Ω) and ${S}_{fin}\left(\Gamma ,\Omega \right)$ in terms of upper semicontinuous functions

### On d-characteristic and ${d}_{\Xi }$-characteristic of linear operators

Annales Polonici Mathematici

Similarity:

### Three periodic solutions for a class of higher-dimensional functional differential equations with impulses

Annales Polonici Mathematici

Similarity:

By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), $t\ne {t}_{j}$, j ∈ ℤ, ⎨ ⎩$y\left(t{⁺}_{j}\right)=y\left(t{¯}_{j}\right)+{I}_{j}\left(y\left({t}_{j}\right)\right)$, where $A\left(t\right)={\left({a}_{ij}\left(t\right)\right)}_{n×n}$ is a nonsingular matrix with continuous real-valued entries.

### On the Rockafellar theorem for ${\Phi }^{\gamma \left(·,·\right)}$-monotone multifunctions

Studia Mathematica

Similarity:

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 $\Gamma :X\to {2}^{\Phi }$ be a cyclic ${\Phi }^{\gamma \left(·,·\right)}$-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 ${\Phi }^{\gamma \left(·,·\right)}$-subdifferential of f, $\Gamma \left(x\right)\subset {\partial }_{\Phi }^{\gamma \left(·,·\right)}{f|}_{x}$.