All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 91

Showing per page

On the extension and generation of set-valued mappings of bounded variation

V. V. Chistyakov, A. Rychlewicz (2002)

Studia Mathematica

We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated...

On the Rockafellar theorem for Φ γ ( · , · ) -monotone multifunctions

S. Rolewicz (2006)

Studia Mathematica

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 .

Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions

Giovanni Anello, Paolo Cubiotti (2004)

Annales Polonici Mathematici

We consider a multifunction F : T × X → 2 E , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.

Polynomial selections and separation by polynomials

Szymon Wąsowicz (1996)

Studia Mathematica

K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.

Polynomial set-valued functions

Joanna Szczawińska (1996)

Annales Polonici Mathematici

The aim of this paper is to give a necessary and sufficient condition for a set-valued function to be a polynomial s.v. function of order at most 2.

Quasicontinuity and related properties of functions and multivalued maps

Janina Ewert (1995)

Mathematica Bohemica

The main results presented in this paper concern multivalued maps. We consider the cliquishness, quasicontinuity, almost continuity and almost quasicontinuity; these properties of multivalued maps are characterized by the analogous properties of some real functions. The connections obtained are used to prove decomposition theorems for upper and lower quasicontinuity.

Remarks on the spaces of differentiable multifunctions

Andrzej Kasperski (2011)

Banach Center Publications

In this paper we consider some spaces of differentiable multifunctions, in particular the generalized Orlicz-Sobolev spaces of multifunctions, we study completeness of them, and give some theorems.

Selection theorem in L¹

Andrzej Nowak, Celina Rom (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let F be a multifunction from a metric space X into L¹, and B a subset of X. We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F(x) for x ∈ B.

Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition

Marek T. Malinowski (2015)

Open Mathematics

We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors). The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect...

Set-valued random differential equations in Banach space

Mariusz Michta (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider the problem of the existence of solutions of the random set-valued equation: (I) D H X t = F ( t , X t ) P . 1 , t ∈ [0,T] -a.e.; X₀ = U p.1 where F and U are given random set-valued mappings with values in the space K c ( E ) , of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.

Currently displaying 61 – 80 of 91