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

Method of averaging for the system of functional-differential inclusions

Teresa Janiak, Elżbieta Łuczak-Kumorek (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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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 ⎧ ( t ) F ( t , x t , y t ) (0) ⎨ ⎩ ( t ) G ( t , x t , y t ) (1)

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.

True preimages of compact or separable sets for functional analysts

Lech Drewnowski (2020)

Commentationes Mathematicae Universitatis Carolinae

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We discuss various results on the existence of ‘true’ preimages under continuous open maps between F -spaces, F -lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.

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.

An elementary proof of Marcellini Sbordone semicontinuity theorem

Tomáš G. Roskovec, Filip Soudský (2023)

Kybernetika

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The weak lower semicontinuity of the functional F ( u ) = Ω f ( x , u , u ) d x is a classical topic that was studied thoroughly. It was shown that if the function f is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on W 1 , p ( Ω ) . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.

Equivalence of multi-norms

H. G. Dales, M. Daws, H. L. Pham, P. Ramsden

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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 ( Ω ) are equivalent, resolving most cases; we have stronger results in the case where r = 2. We also show...

H functional calculus for sectorial and bisectorial operators

Giovanni Dore, Alberto Venni (2005)

Studia Mathematica

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We give a concise exposition of the basic theory of H 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 ( T , . . . , T N ) when f is an R-bounded operator-valued holomorphic function.

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 , . . . , 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.

A pair of linear functional inequalities and a characterization of L p -norm

Dorota Krassowska, Janusz Matkowski (2005)

Annales Polonici Mathematici

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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.

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 ( ) -tempered functions on + (M. Hemdaoui, 2017) equipped with its natural convex vector bornology is useful for functional calculus.

CM-Selectors for pairs of oppositely semicontinuous multivalued maps with p -decomposable values

Hôǹg Thái Nguyêñ, Maciej Juniewicz, Jolanta Ziemińska (2001)

Studia Mathematica

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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 ( T , E ) -decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, L p ( T , E ) is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x)...