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On a fixed point theorem for weakly sequentially continuous mapping

Ireneusz Kubiaczyk (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let E be a metrizable locally convex topological vector space x ∈ E, and let D be a closed convex subset of E such that x ∈ D. In this paper we prove that the weakly sequentially continuous mapping F: D ∪ D which satisfies V̅ = c̅o̅n̅v̅({x} ∪ F(V))⇒ V is relatively weakly compact, has a fixed point. Employing the above results we prove the existence theorem for the Cauchy problem x'(t) = f(t,x(t)), x(0) = x₀. As compared with the previous...

On a fixed-point theorem of Cellina

Stephen Simons (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota mostriamo come un teorema di esistenza per funzionali lineari porti un nuovo teorema di punto fisso che generalizza un teorema di punto fisso di Cellina.

On a formula for the jumps in the semi-Fredholm domain.

Vladimir Rakocevic (1992)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we prove some properties of the lower s-numbers and derive asymptotic formulae for the jumps in the semi-Fredholm domain of a bounded linear operator on a Banach space.

On a function that realizes the maximal spectral type

Krzysztof Frączek (1997)

Studia Mathematica

We show that for a unitary operator U on L 2 ( X , μ ) , where X is a compact manifold of class C r , r ∈ ℕ ∪ ∞ , ω , and μ is a finite Borel measure on X, there exists a C r function that realizes the maximal spectral type of U.

On a functional equation with derivative and symmetrization

Adam Bobrowski, Małgorzata Kubalińska (2006)

Annales Polonici Mathematici

We study existence, uniqueness and form of solutions to the equation α g - β g ' + γ g e = f where α, β, γ and f are given, and g e stands for the even part of a searched-for differentiable function g. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.

On a general bidimensional extrapolation problem

Rodrigo Arocena, Fernando Montana (1993)

Colloquium Mathematicae

Several generalized moment problems in two dimensions are particular cases of the general problem of giving conditions that ensure that two isometries, with domains and ranges contained in the same Hilbert space, have commutative unitary extensions to a space that contains the given one. Some results concerning this problem are presented and applied to the extension of functions of positive type.

On a generalization of a Greguš fixed point theorem

Ljubomir B. Ćirić (2000)

Czechoslovak Mathematical Journal

Let C be a closed convex subset of a complete convex metric space X . In this paper a class of selfmappings on C , which satisfy the nonexpansive type condition ( 2 ) below, is introduced and investigated. The main result is that such mappings have a unique fixed point.

On a generalization of Lumer-Phillips' theorem for dissipative operators in a Banach space

Driss Drissi (1998)

Studia Mathematica

Using [1], which is a local generalization of Gelfand's result for powerbounded operators, we first give a quantitative local extension of Lumer-Philips' result that states conditions under which a quasi-nilpotent dissipative operator vanishes. Secondly, we also improve Lumer-Phillips' theorem on strongly continuous semigroups of contraction operators.

On a generalization of W*-modules

David P. Blecher, Jon E. Kraus (2010)

Banach Center Publications

a recent paper of the first author and Kashyap, a new class of Banach modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the Riesz representation theorem for Hilbert spaces), which in turn generalize Hilbert spaces. In the present paper, we describe these modules, giving some motivation, and we prove several new results about them.

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