Continuity of spectrum and spectral radius in algebras of operators
Continuity of sublinear operators on F-spaces.
Continuity of superposition operators on and
Continuity of the Drazin inverse II
We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.
Continuity of the spectrum of norm-normal matrices
Continuity of the superposition of set-valued functions.
Continuity properties of best analytic approximation.
Continuity properties of nonlinear mappings
Continuity properties of projection operators.
Continuity versus boundedness of the spectral factorization mapping
This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.
Continuity versus nonexistence for a class of linear stochastic Cauchy problems driven by a Brownian motion
Let denote the generator of the rotation group in the space , where denotes the unit circle. We show that the stochastic Cauchy problem where is a standard Brownian motion and is fixed, has a weak solution if and only if the stochastic convolution process has a continuous modification, and that in this situation the weak solution has a continuous modification. In combination with a recent result of Brzeźniak, Peszat and Zabczyk it follows that (1) fails to have a weak solution for all...
Continuous and compact imbeddings of weighted Sobolev spaces. I
Continuous and generalized solutions of singular partial differential equations.
Continuous Branches of Positive Solutions for a Class of Nonlinear Second-Order Differential Equations.
Continuous data dependence for an abstract Volterra integro-differential equation in Hilbert space with applications to viscoelasticity
Continuous dependence of solutions for ill-posed evolution problems.
Continuous dependence on data for quasiautonomous nonlinear boundary value problems.
Continuous dependence on parameters for second order discrete BVP’s
Using Fan’s Min-Max Theorem we investigate existence of solutions and their dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the relevant Euler action functional.
Continuous dependence on parameters of the fixed points set for some set-valued operators
In this paper we extend the notion of I⁰-continuity and uniform I⁰-continuity from [2] to set-valued operators. Using these properties, we prove some results on continuous dependence of the fixed points set for families of contractive type set-valued operators.
Continuous extension of order-preserving homogeneous maps
Maps defined on the interior of the standard non-negative cone in which are both homogeneous of degree and order-preserving arise naturally in the study of certain classes of Discrete Event Systems. Such maps are non-expanding in Thompson’s part metric and continuous on the interior of the cone. It follows from more general results presented here that all such maps have a homogeneous order-preserving continuous extension to the whole cone. It follows that the extension must have at least...