On Some Classes of Operators II.
On some classes of Operators on Hilbert spaces
On some classes of Volterra integral equations in Banach space
On some common fixed point theorems of Aamri and El Moutawakil in uniform spaces.
On some consequences of a generalized continuity
In normed linear space settings, modifying the sequential definition of continuity of an operator by replacing the usual limit "" with arbitrary linear regular summability methods we consider the notion of a generalized continuity (-continuity) and examine some of its consequences in respect of usual continuity and linearity of the operators between two normed linear spaces.
On some constructions of new triangular norms.
We discuss the properties of two types of construction of a new t-norm from a given t-norm proposed recently by B. Demant, namely the dilatation and the contraction. In general, the dilatation of a t-norm is an ordinal sum t-norm and the continuity of the outgoing t-norm is preserved. On the other hand, the contraction may violate the continuity as well as the non-continuity of the outgoing t-norm. Several examples are given.
On some dilation theorems for positive definite operator valued functions
The aim of this paper is to prove dilation theorems for operators from a linear complex space to its Z-anti-dual space. The main result is that a bounded positive definite function from a *-semigroup Γ into the space of all continuous linear maps from a topological vector space X to its Z-anti-dual can be dilated to a *-representation of Γ on a Z-Loynes space. There is also an algebraic counterpart of this result.
On some discontinuous fixed point mappings in convex metric spaces
On some ergodic properties for continuous and affine functions
Two problems posed by Choquet and Foias are solved:(i) Let be a positive linear operator on the space of continuous real-valued functions on a compact Hausdorff space . It is shown that if converges pointwise to a continuous limit, then the convergence is uniform on .(ii) An example is given of a Choquet simplex and a positive linear operator on the space of continuous affine real-valued functions on , such thatfor each in , but does not converge to 0.
On Some Fixed Point Principles for Cones in Linear Normed Spaces.
On some fixed point theorems.
On some fixed point theorems in Banach spaces.
On some functions that map each generator of a -semigroup into the generator of a holomorphic semigroup.
On some geometric constants and the fixed point property for multivalued nonexpansive mappings.
On some inequalities in normed algebras.
On some local spectral theory and bounded local resolvent of operator matrices
We extend and generalize some results in local spectral theory for upper triangular operator matrices to upper triangular operator matrices with unbounded entries. Furthermore, we investigate the boundedness of the local resolvent function for operator matrices.
On some matrix Inequalities in Banach Spaces
On some modification of the Levinson operator and its application to a three-point boundary value problem
On some new embedding theorems for some analytic classes in the unit ball.
On some new spectral estimates for Schrödinger-like operators
We prove the analog of the Cwikel-Lieb-Rozenblum estimate for a wide class of second-order elliptic operators by two different tools: Lieb-Thirring inequalities for Schrödinger operators with matrix-valued potentials and Sobolev inequalities for warped product spaces.