Common fixed points of weakly contractive and strongly expansive mappings in topological spaces.
Let K be a closed convex cone with nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. If F t: t ≥ 0 is a regular cosine family of continuous additive set-valued functions F t: K → cc(K) such that x ∈ F t(x) for t ≥ 0 and x ∈ K, then .
We investigate the long-time behaviour of solutions to the Korteweg-de Vries equation with a zero order dissipation and an additional forcing term, when the space variable varies over , and prove that it is described by a maximal compact attractor in .
The definition of n-width of a bounded subset A in a normed linear space X is based on the existence of n-dimensional subspaces. Although the concept of an n-dimensional subspace is not available for metric trees, in this paper, using the properties of convex and compact subsets, we present a notion of n-widths for a metric tree, called Tn-widths. Later we discuss properties of Tn-widths, and show that the compact width is attained. A relationship between the compact widths and Tn-widths is also...
We prove criteria for relative compactness in the space of set-valued measures whose values are compact convex sets in a Banach space, and we generalize to set-valued measures the famous theorem of Dieudonné on convergence of real non-negative regular measures.